Hey everyone, Nate Chance here. We're going to talk about Pokemon and Junichi Musada here or Masuda or whatever. I know I butcher these Japanese names all the time. I apologize about that. There's a lot going on out in the gaming world that we could be talking about today, of course. There's some some interesting stories about Sony Skipping E3 again, which I guess they did it last year. So is that surprising? I don't really know that it's that surprising. But we could talk about that maybe another time. Some other rumors and reports out there potentially Pikmin 3 coming to switch and all that. We'll we'll get into that maybe in some future videos, but I want to talk about this because I am a video game fan first and foremost. I am a gamer. I like talking about video games. I like playing video games. I like watching other people play video games at times. And I like discussing the video game industry. Hence why I have this YouTube channel in the first place. And what I don't like about video game fans at times is we as a collective, this isn't to point out anyone individually, have a tendency to go too far. There's nothing wrong with criticizing games. There's nothing wrong with, you know, lobbing critiques and and doing so in in ways that make sense. But sometimes we do things that it just gets kind of old. It gets kind of stale. It's it's old hat. It's old news. People don't want to consistently hear about the same thing over and over again. Especially, you know, going on six months, seven months, eight months after a game come out, etc. Because it's not going to change the reality of the situation at this point. They already know our critiques. In this case, Junichi Masuda is trying to enjoy his birthday. But in trying to enjoy his birthday, people can't stop bitching at him about missing Pokemon from the Pokedex. This has been the biggest controversy of Pokemon Sword and Shield period is it is the first new generation of Pokemon games that does not have a global Pokedex somewhere. There's no ability to import every Pokemon that's ever existed into the game. Even though they're not, you know, normally available in the game, there's always been a way to have like this big national decks. And in this case, with Pokemon Sword and Shield, that's not possible. And fans are probably even more infuriated, if I had to guess, at the announcement of the DLC. Some fans are happy with the DLC, but others view it as there are some of the old Pokemon coming back in the DLC. And so they feel like Pokemon were cut to be resold to us in DLC. And that's kind of where the quote-unquote new wrinkle to be an upset about the national decks is coming from. But again, it's not a new complaint. It's just repackaging an old complaint in a new way. So let's get into the story as Nintendo Life reported it by Damian McFerran. I'll have a link to this article down below. Credit to Nintendo Life, they do excellent work out there. While Pokemon Sword and Shield has been a smash it all over the world, its release has been dodged by debates over what has become known as Dexit, a.k.a. the removal of legacy Pokemon from the games national Pokedex. Prior to launch developer Game Freak announced that it had made a decision to remove certain monsters from the game and later stated that it would be doing the same for future installments, which sparked backlash from certain parts of the community. Very, very vocal backlash. Not backlash that actually led to bad sales, but backlash that kind of uprising you get on the internet is just relentless. It doesn't stop. It still isn't stopping. The debate was revived last week when it was confirmed that the upcoming expansions, the Isle of Armor and the Crown Tundra, will feature over 200 monsters from past Pokemon games. Game Freak has stated that these monsters will still be available to those who don't purchase the expansion pass, so that's a key point. I get to trade for them, I believe. The news has still attracted a small but vocal negative response. Game Freak co-founder and head of development Junichi Masuda, who was working on every mainline Pokemon game since the series began, is getting a little heat on his birthday over the whole thing. And this was spotted by Video Game Chronicle. I wish him happy birthday on Twitter, which makes sense. You're wishing happy birthday to a public figure, an important person in the industry, maybe your Pokemon fan. Obviously, we do this for Agee and Omo for Zelda. We do this for Shigeru Miyamoto and others. Wishing happy birthday on social media is a pretty normal thing. So it's kind of like fans are reaching out and saying, hey, happy birthday. Big deal. That's kind of a stream of positivity to start your day. Do it for me as well on social media on YouTube. There'll be random comments saying, hey, happy birthday for those that remember that it happens to be my birthday. But one user, the only one that Masuda has replied to directly, and this is how you know he saw this comment. He actually replied to it. At the time of writing, decided to take in the task for the decision to remove old Pokemon so that you can make money from DLC. A clear reference to the recent Expansion Pants announcement. Masuda responded, it's a public holiday today, and it's his birthday. Can you let me relax? See, I'm fine in general. You want to lob a bunch of criticism at Game Freaks official Twitter account. But when it comes to the individual level of someone on social media, an individual person who represents an entire company, but isn't always the one making every single decision in that company, to keep going at him. Let's just open this tweet. It is in Japanese, so we're going to be using the translate feature on Twitter. So let's open this up and see the string of tweets here. So let's see here. It started with this tweet right here. So let's translate that tweet. It says happy birthday. So someone said happy birthday, and I assume that this was retweeted by Masuda. He retweeted the happy birthday. So this is on a tweet that's specifically about his birthday. This is what's so frustrating. I know people are going to lobby criticism at individual creatives all the time. But this is a post, a tweet directly about his birthday. A fan wished him happy freaking birthday. Alright. Let's see his official response here. Said thank you. So again, he retweeted, commented, said thank you for wishing him happy birthday. It's all happy vibes here, right? A fan reached out and said happy birthday, posted some Pokemon stuff, blah blah blah. Everything's all right in the world. But then this guy has to come around and please give a word about the removal of old Pokemon to make money as DLC. And not only that, it has 503 retweets and 368 likes. So it's not like this is a post that's being ignored. This is a person responding to a birthday tweet with demands and criticism about Pokemon. Responding to a birthday tweet. Let me repeat that with like criticism about Pokemon DLC. About removal of Pokemon. There are ways, folks, to be human about this. Because I think this is really prevalent on the internet. I don't think anybody would say this to his face if they knew it was his birthday. If Genichi Masuda is out celebrating his birthday and you're at the birthday party, chances are you're not going to say a damn word about this. You're just going to say happy birthday, thanks for all the memories, all that stuff. Maybe give him a present or something.  People will not walk up to him in person knowing it's his birthday at a birthday celebration. This is a birthday celebration post. And do this. But that's not the way the internet works because we're all anonymous. I mean this person's username definitely doesn't look like a real name. It also has a cartoon avatar or an anime avatar or whatever it is. Maybe it's from a specific anime I don't recognize. But that is not proper etiquette for talking to another human being. And then I think on the internet we forget that these are real humans, they're not robots. Just because we're click-clacking away on a keyboard or typing on phones or whatever doesn't mean that these aren't people. I mean he clearly was talking to folks on Twitter for Android. These are people. These are actual people with real feelings and real lives. And they go well beyond what they do for a job. Gotta remember, him working at Game Freak and for the Pokemon company is his job. It's not who he is as a person. Yes, a lot of us can closely associate our work with who we are but we are not the sum of our work. We are the sum of everything else in life work being part of that equation. So I look at this as just a completely inappropriate way to lobby this criticism. You wanna tweet at him the criticism. You wanna respond to a different tweet that's about the Sword and Shield DLC or something and lobby that criticism. Fine. That's like the appropriate way to do it. Give the critique on the things that actually have to do with what you're critiquing. This is about a man's birthday. A man's birthday. And you had to bring this critique out. His direct response as translated by Google. It's a holiday today and it's a birthday, his birthday. And he let me relax. And this is even the worst. Like this guy, Herschel Nova. Look, he said, if you wanted to relax you wouldn't be looking at Twitter. Social media is a part of our everyday lives. Most of our everyday lives.  YouTube is technically a social media platform. So you're making YouTube part of your day today if you're watching this video. We all have our phones. Some of us use Twitter, Instagram, Snapchat. There's a billion like social, you know, Facebook. Social media is out there. Even ones that I've vaguely heard of but I have no experience with. Even for like business people, you know, that programmers that we have linked in and all that. It's interesting to me to see that the criticism is being excused because he chose to look at Twitter on his birthday. Something that is integral to our daily lives.  Even though there's some genuine people out there wishing this guy happy birthday and making him smile. So he should stop because others can't control themselves. Or maybe we should just talk about, I don't know, being decent human beings, leaving the man behind on his birthday. I have a huge problem with this type of criticism and this method of criticizing. Something with video games. It just doesn't make sense to me.  These people are just relentless. Relentless. If we give this man another chance he would just make even more BS excuses to cut content again. Like, it's just non-stop. This is on the tweet about a man's birthday. Why can't we be decent human beings on the internet? I seriously ponder this. Why can't we be decent humans on the internet and be, like, understanding of people and understand that we're all different and that, like, our lives aren't just about a singular thing?  People always complain, blah, blah, blah, blah. The thing is, I get the critiques, I understand the criticism. I get that it's not a good look to cut all these Pokemon and then resell them to you as DLC. I understand that I get the criticism and I get why people are frustrated with it. But I also think that there's a time and a place. I firmly believe there's a time and a place for this kind of criticism. There's a time and a place to talk to Masuda about this. And while social media is going to be flooded with people like this, and Masuda has to understand that, you know, he's the leader of a really popular video game.   And maybe he needs a little bit of a thicker skin. I also think that just because maybe he can handle the situation better doesn't mean that it's a valid excuse for doing this. Let the man celebrate his birthday, including on social media, including with fans of his work. It's okay for him to celebrate that with fans of his work. I don't think it's okay to go on a celebration post about an individual's birthday, not even birthday of Pokemon, his individual birthday and blast him. Put him on blast. Get attention for yourself.   And that people need to stop doing this. I've had it done to me. Others have had it done to them. All public fitters have it done.  And my plea to you Pokemon fans, my plea to any of you fans out there is that we lobby our critiques and our criticisms in the right places in the right forums at the right times. I think we should all be able to agree that on a post about someone's birthday, someone's actual personal birthday, then maybe we should leave out the critiques of some of their work because the person is not the same as the work. That's really all I got for you guys for this video. Thank you so much for tuning in. Let me know what you think about throwing the comments below because this happens a lot on the internet. And it frustrates me every single time. And I really want to hear your guys' honest to goodness thoughts even if you disagree with me. It's okay. Let's have a conversation. Let's spark a debate. So go on the console. Let me know what you think. I am Nate Jantz. Like, subscribe, comment. Hit that little bell icon if you want notifications on every video and every live stream. And hey, I'll catch you guys all in the next video, which I already named at the very beginning. A whole bunch of topics I still need to talk about. So man, things are moving faster now. There is just gaming news flying everywhere. It's going to be a great 2020. Let me tell you. Peace out, everyone.


what's going on guys it's your boy dpj here today with another destiny video and today I've been in my horror mode rafting the machine hunter looting results and I got some badass more fucking shit but before we get into the video if you guys do enjoy hitting that like button is much appreciated let's aim for 4,000 likes that'd be absolutely insane okay then so basically her mode dropped late last night well not late last night what was late that kind of late last night for us in the UK which is a 10 p.m. for people who work the next day and have school it is pretty late but it wasn't late for me but yeah and so it's dropped at 10 p.m. we finished it about a couple hours after that didn't really struggle to be honest I tell you one thing though the night falls are a lot harder than the herok mode raid that damn shield rather saw a lot of burn is a pain in the ass and I was the glitch but but still it's literally one shot from every enemy it's ridiculous but yes the rafting machine raid loot results let's get into it okay so from volzik phase one I got a legendary engram from the secret chest I got another legendary engram and a 385 gravity on 4th exotic helmet playing on her own mode from the chests you do have a chance of getting the normal exotics and the heroic exotics the normal exotics drop up to a 35 and their heroic exotics drop up to a 400 this unfortunately was a 385 normal exotic moving on to volzik phase two and I got a legendary engram and I got a 396 attack zeal vector sidearm I also got a 385 attack quantity plasma shotgun the zeal vector sidearm has reactive reload and quick reaction grade increased agility while the reactive reload perk is active the thing is I just don't use sidearms I don't like sidearms and this thing could be much much better use infused so that's what it's going to use for from the see the cash chest I got the ex machine ass sniper dropping a 396 attack this one's got a spray and play and wait for it reloading this weapon when the magazine is empty grants a larger than normal magazine this is strictly though a PvE sniper I mean the zoom on it is ridiculously long and far and shit it's just ridiculous definitely a PvE sniper does decent damage as well and with wait for it when you get a larger than normal magazine it does do great damage when that boss encounters moving on and from the second and third chest I got legendary engrams from the death Sanboni a 396 if materia heavy machine gun also got a 385 attack sand and play rocket launcher as well as a legendary engram but if material has to perk triple tap and triple double when triple tap perk is triggered an extra bullet is transferred from the users into the magazine now at first when I saw this and thought this perk on a heavy machine gun that shoots absolutely ridiculously quick there could have been a lot better things added to it but to be honest isn't too bad it triggers quite a lot giving you a few extra bullets I mean nothing spectacular but still it's better than fuck all and it's another thing that works the bus because obviously extra damage to fallen so I will keep the sink and level this bad boy up from the see the cash chest I got the spliced then all mainly a vest dropping at 395 defense offering interact and discipline so not bad at all from the fourth secret chest I got a legendary ingram from axis phase one I've got a perfected see the shard artifacts dropping at 396 defense and I got a 385 defense ghost shell from axis phase two I got 395 defense splice Nanomania cloak and from the see the cash chest I got 396 attacks deal modular pulse rifle this thing is a beast a PvE beast that is with full auto and sign of four landing three burst on a target causes the fourth burst to do extra damage pretty useless in PvP I mean unless you're fighting against a Titan when you're in that handle solo something like that but I reckon this could be quite good against buses I will have to level it up though and try it out and let you guys know but guys that is it for my first heroic mode completion done on my hunter I will be doing my titan and warlock later today so I expect another loot video when I do do on them but guys if you've done it let me know what you've got down below in that comment section anyone get the hand cannon let me know but guys hope you enjoyed the video do hit that like button under appreciate the support thanks for stopping by as always and I'll catch you on that next one


Thank you very much. Okay, so last time we finished with the formula with the Analog of the Gibbs property for the sign process. So let us write again. So we consider is a conditional measure the conditional measure at this moment for the sign process, but in fact Precisely what I want to discuss today is the degree of generality of this result is the That's the conditional measure of the sign process by fixing the configuration in the complement Of an interval So fixing the configuration in the complement of an interval. So in fact in Pavel's talk yesterday, we Saw a detailed explanation and so I don't need to give it here a detailed explanation of why the number of particles in the interval is fixed So of the rigidity of Goshen Peres. So we have particles x fixed particles in the environment in the outside So x fixed So we fixed this is the part of configuration of x in restriction to r without i This is the interval i and so the conditional measure is obtained by fixing these and by allowing these to move their total number is fixed as Pavel explained to us Yesterday and so the conditional measure is the following also so Yesterday in At least we saw some elements of the argument and I will explain The remainder of the argument Okay, so this is the conditional measure and the infinite product is understood in principle failure So and I explained Yesterday, I think in some detail that the The fact on which this Statement is based is the relationship between palm measures So the relationship between palm measures of the sign process which I wrote like this is equal to product of T minus Excuse me product of x minus p x minus q Square x and x product is understood in principle value Which in turn was derived from the fact that the palm subspaces That the palm subspaces are Related so L so L the range of the sine kernel let us recall that the range of the sine kernel is just the Paley Wiener space so the space of functions whose forest Fourier transform is supported on minus pi pi and so The we consider the space PW of P being this space of functions phi in Paley Wiener Such that phi of P is equal to zero and then we have the relation PW of P is equal to X minus p x minus q PW of q Okay, so and then Just yesterday. I just said that from this one obtains this but in fact this step Requires a certain Effort and I will say very briefly. I will just say very briefly The effort that it takes and then I will illustrate by some examples How in different models one obtains different results? So let me let me first explain in the case of the sign process. So, okay, maybe two Stress immediately is there need for some Extra effort let me point out That so for sign process this multiple functional converges in absolute value excuse me in principle value as in fact that is written here But for example for every process it doesn't for every process this mode as this diverges because the airy particles Well, there are very few in the negative some axis. There are very many in positive some axis So of course there is a way out of it. There is some need of regularization and this is exactly what I aim to explain So what I'm trying to say is that in the so we proved Let me put it on the other blackboard for reference purpose. We proved the statement that if I Make a transition so so I have a space L and I have a space square root of GL So and this is the projection on the space L is denote by pi the projection of the space square root of GL is denote by pi G then as We discussed in great detail The Radon Nicodem derivative so the process the the determinational point process is corresponding to pi and to pi G are equivalent and the Radon Nicodem derivative is precisely the multiplicative functional corresponding to the function G the point however is that it is often necessary one often it is often necessary to Consider situations when these multiplicative functionals understood literally diverges and this is the Specific example is the example of the airy of the airy point process where such multiplicative function will simply diverge There is a need for regularization. Yes Is an infinite configuration? Yes, they could be say again. Excuse me. No, of course not. It is a it is an infinite configuration. Yes No, no Yes Say again, excuse me. Yes. That's quite precise That's exactly what I'm coming to So I'm answering your question right now In fact, the statement will be the statement will be understood almost surely the convergence will take place almost surely That's right. We'll take place for almost all configurations. And so as you say as you say one needs to Play some conditions on the kernel in order that the convergence take place almost surely with respect to this determinant point process But in fact as I say There are some nuances because there are some nuances. So this infinite let me put it this way So this statement is completely universal. It's also true for airy kernel is true for many examples on the other hand the multiplicative functional Might diverge and does diverge in examples as it diverges for the airy kernel So it does converge for the sine kernel. That's why I started with this example But for the airy kernel it diverges So I will need to have a procedure of Irregularization of this multiplicative functional, which I am now going to explain. Yes, and I have an answer for this Yes Yes, here it is. So the axis are The axes are distributed according to the underlying determinant point process the axes are a realization of the underlying point process of The let's say of the sine process So the realization of the sine process and I will explain the property of the Sine process which ensures that almost every realization Is such that this product converges in Principal value in this case The measure on the t's is of course random because in fact that is quite precise. So because x is a random configuration Of course the condition that's quite precise a conditional measure is a random measure because the condition itself is random That's quite precise. Of course, that's exactly right. It's a random measure. That's quite precise. Yes So it's a random measure. Yes. So first I fix a realization of the sine process and then so which is a random realization Then to this realization is Assigned the conditional measure That's quite precise. Yes. Okay, so I proceed so and let me explain So let me explain. So what is my purpose now my purpose now is to give meaning to this Expression even when the multiplicity function itself diverges so we shall see right now That's what I will explain a little bit briefly that it is possible to have This formula still to be true even when the multiplicity function itself is not defined but is defined a weak version of multiplicity functional and Regularized multiplicity function so and this is precisely what I'm going to explain and then I will also illustrate by some examples Which show how regularization of multiplicity functionals Takes different forms for different models regularization of multiplicity functions So let me just start with formula So I want to consider multiplicity functions But multiplicity functionals are Laplace transforms of additive functionals and so I let me start with additive functionals and so Let me first regularize additive functionals and for this let me point out that if I have an additive functional so again these formulas we saw in Pavel's talk and also in other Talks, so if I have an additive functional Then the expectation of the additive functional is of course the integral of F DDT Let me write off. Why do I so for the for this variable while The variance and this is a formula that we saw several times The variance of SF is In fact the double integral of F of X minus F of Y square times pi Of X of Y square DX dy well to put it rigorously D mu effects D mu of Y here I am in this formula holds in the full generality. So I have that is to say a projection pi From some L2 in you onto some subspace L and the corresponding Determinant all point process be by This is a direct verification using well in fact the definition using in fact the definition and In fact Pavel wrote to us yesterday a more general formula for arbitrary point process For which this is a corollary because the first term in the general formula is zero in the determinant case okay, so One can see by looking attentively at this formula that it is quite possible So this is essentially a so belief one-half norm So in many in many yes, no yes. Oh, there is there is of course. Yes. Thank you very much. Yes. Yes. Yes. I wrote it I wrote it In yes, of course. Thank you very much. Yes. Thank you very much. Yes Yes, in fact I wrote it incorrectly so The variance is essentially so belief one-half norm But it is very easy to give an example of a function for which which fails to be Integrable but for which so belief one-half norm is finite It is very possible to have a function which is not integrable But for which so belief one-half norm is finite and to such function So if F So, let us write the following let us consider the map F Going to SF minus expectation of SF The letters denoted by SF SF bar and so then this map SF bar is well defined is Well defined Can can be extended by continuity for all F For all F for which The right-hand side of star is finite, but these functions may or may not be Integrable and in fact the function one over X is precisely is precisely an example a case in point where this integral is well in strict sense not defined But this integral is perfectly well defined and so precisely one can define The regularized multiplicative functional at this point. So at this point a regularized multiplicative functional a regularized multiplicative functional Let me write it this way expectation of exponential SF let me write it in this way is Can be defined as in fact Well clearly I define it How do I say I define bar Times Shell of integral of F Well, this is a tautology But except it is possible Let me let me write it this way. Excuse me. Let me write it this way. So this is a tautology except This side can be can be well defined in Situations in which neither this nor this is well defined So this is exactly the same situation as what I wrote in fact for for the Hilbert Carleman Hilbert Carleman regularization of the determinant So this is precisely the same situation this determinant can be well defined when neither this nor this is Well defined when either this nor this is well defined So and precisely this this regularized multiplicative function as well defined even in situations when neither this nor this well defined by a certain limit transition So in particular if so in particular Yes, I'm doing it. I'm doing it in particular exactly in particular if a Colonel if a Colonel pi on our on our Satisfies satisfies what satisfies that the integral of pi xx One plus x squared is less than is fine. It's so observed that it is x square Yes, so for example the Eric Arnold satisfies this Then the regularized then the regularized multiplicative functional the regularized multiplicative functional multiplicative functional is well defined So the regularized multiplicative function is well defined So product regularized x minus p square Well defined. So is well defined this one with respect to the measure P Q of course. Yes. So there are there are there is a there are two nuances here So there is a nuance. There is a nuance at zero. So at Q at Q Yes, so The Function obviously has a zero at Q This however is not a problem because let us recall that the function P Q XY the for the formula of Shirai and Takahashi that we wrote last time here it is so this formula Shows to us that in fact one can see that they On the diagonal on the diagonal at Q The kernel has a zero in fact a zero of order two Not only does it have a zero it has a zero of order two. So there is no problem. There is no problem with defining The functional There is no problem with the neighborhood of zero the problem is Perhaps with the convergence the problem is with the convergence, but again using this regularization using this regularization and Using this formula using this formula one Can't define the regularized multiplicative function and So the general the general form of this statement. So in particular, let's even look at this case. So obviously again For a function one over X for function one over X this quantity is completely finite For function one over X this quantity is completely finite So the regularized multiplicative functional is well defined whereas the non regularized isn't and so the The formula holds in Complete generality the formula holds in complete generality With a certain correction so in full generality, let me now formulate. So let me now formulate the general The general case of the formula Let me erase the procedure of regularization So the general The general case of the formula the general form of the formula. So here I Consider a kernel having integrable form or equivalently a Kernel satisfies weak division axiom weak division axiom, so if phi is an L of P Then Phi over X minus Pi is an L So consider this form. So the other the other direction is enjoying to work with Roman Romanov So in general with Roman Romanov, okay So we consider this integrable kernel and we have this regularity assumption I should say this regularity assumption is sometimes not Verified I should say so there is technical difficulty. So let me Restrict myself in this discussion to one dimensional real case But let me point out that this this formula this is not verified in one-dimensional complex case The result is true, but this assumption doesn't hold in fact Let me allow me please allow me to restrict myself not to give rigorous formulation, but to just limit myself to Non-rigorous formulation so in just in the same way as Regularization of determinant can go further. So the expression determinant 1 plus a can be regularized Further so one So one can write it as e to the trace a times determinant One to one plus a but one can also write it as e to the trace a plus one-half trace Exterior square of a times determinants three one plus a and the advantages the determinants three one plus a is at this point Defined for operators, which are not even Hilbert Schmidt, which are in search at in class and so on one can continue this game It doesn't seem necessary in applications at this. However, the case of So I mean going further hasn't been so far necessary in examples But the case when this example doesn't hold when this condition doesn't hold does arise in examples and may and namely when we consider the Determined by process corresponding to Fox space which we saw several times at this conference when we consider Just similar complex situation one-dimensional complex situation So let me write it here. So the kernel is Z w is e to the Z w bar minus episode square square To so this is just the Kernel in the fog as they're producing kernel of the Fox space So what does mean Fox space it is space of functions square integrable with respect to the Gaussian weight So it is generated by a monomial z to the k and so the generating function is like this Okay So in this case this assumption will not hold all the formalism go through but regularization must go Even one step further must go to the third to determine on three and this was done in joint work with Yanxi she So, okay, so let me just point out that Yes, that from here from here We have this so this just follows from the weak division axiom. So there is no question about this There's excuse me. I wanted to say excuse me. So this also, but I wanted to say this so so the expression as the expression L of P is equal to X minus P X minus Q L of Q this this just follows directly from the weak division X from the weak division axiom and so using their regularization of Using the regularization of multiplicative functionals one is able to Obtain this formula In the same way for regularized multiplicative functional So even if even if regularized multiplicative functional exists in this formula still holds this formula still holds and Then one obtains this same formula, but for regularized multiplicative function regularized Functional and then one obtains this formula it looks the same But with important difference, so let me write it P it looks the same But here I put regularized so not principle value anymore. It's just regularized multiplicative functional So again regularized in the sense that the exponential of the trace is subtracted So this so in fact meaning of regularization is very clear This product diverges But if you subtract exponential of the trace of the logarithm it converges So this is the meaning of regularization and there is just one more Correction term. So I wrote dti. In fact, I have to write Row of ti where row is a function which only depends on Row is a function which only depends on so there is a way. Let me I wrote roll Let me denote it w actually w by excuse me w So there is this weight function which only depends on So and this so in this generality one has this general formula with regularized multiplicative function and with this function w So this function w in some examples, it's possible to find it. So let's consider examples. So let me consider an example Example so I will consider two examples one example without regularization and one example with regularization So example without regularization is example of the Bessel kernel So Bessel kernel. So this is the kernel which again we saw several times in The talks today During this conference. So I write Square root of x. I write it in slightly different form, but it comes down to the same yes Yes, and also it is even more convenient to write the Bessel kernel in the following form Is the integral of one fourth? Zero to one J s square root of Tx J s square root of T y DT Okay, so what does it mean Bessel kernel the Bessel kernel is the kernel of It's very similar spectral projection very similar spectral projection To the sine kernel so the sine kernel is the spectral projection on paleo inner space Which is the space of functions such that the Fourier transform is supported in minus pi pi Support of the Fourier transform is in minus pi. So this is the Space for the sine kernel for the Bessel kernel instead of the Fourier transform has to consider the Hankel transform H s f of lambda is equal to one half integral from zero to infinity f R J s square root of lambda r D r and by the way in many sources for example on Wikipedia if you read The definition of Hankel transform it's for some reason Reason written s bigger than one half and they could never understand why people write as bigger than one half In fact, it's perfectly well defined if I says bigger than minus one So it is really a source of great mystery to me why why people write s as Bigger than minus one half as bigger than minus one strictly bigger than minus one It's Hankel transform perfectly well defined and it's involutive So the Fourier transform you have the Fourier transform and the inverse Fourier transform, but for Hankel transform It is just an involution It is just an involution. It's wonderful transform So it's obviously just as the Fourier transform. It's a spectral projection Corresponding to the operator of the Bessel equation Let me not write it down. We don't need it for the purpose of this class the point is that of Course well the kernel is integrable here. It is you can see that the kernel is integrable The kernel arises of course a scaling limit of orthogonal polynomials Indeed which orthogonal polynomials? They for you one can consider either Yacoby polynomials Yacoby polynomials or Laguerre polynomials for computations It's often easier to work with Laguerre polynomials But the Yacoby polynomials come down to the same. So this is classical asymptotic of Heine-Meyler Heine-Meyler asymptotics 1847 Just Yacoby polynomials converge to Bessel function and one can see it very nicely Yacoby equation converges to Bessel equation So there is spectral projection There are so excuse me just as a remit polynomials converge to the sine function Yacoby polynomials converge to the Bessel function So it shouldn't very greatly surprises that the Christopheles der Buchernel converges to this kernel So the kernel has integral of form So again, it shouldn't very greatly surprises that the weak division axiom holds. Well, it comes down to the same and At this point also the relation between palm measures holds. So this is just a corollary of the weak division axiom That's corollary of the weak division axiom and at this point also this result holds in fact here There is no regularization the multiplicative functional converges in normal way So in fact here they one can check that the integral of Js xx over 1 over x 1 plus x is finite Is finite one can check this So this is maybe clearest from here because one can see that there is a certain power decay for the Bessel kernel it decays in a power way. Well, it's also clear here so one can maybe easiest if one writes it with derivatives and Then it is still clear that there is a little bit of power decay and Which however is enough to have this Formula so all the products converge Literally and the function rho pi W pi of t is equal to t to the s is equal to t to the s The function w by t is equal to t to the s Okay, so this much this much for the Bessel kernel it all holds literally here So second example, I would like to consider is the gamma kernel the gamma kernel of bradyn and Alshansky Where in fact regularization takes a certain form So gamma kernel Yes, yes, sorry excuse me second Very excuse me W okay, this is very good question. So in this case. So, okay, so the function comes from okay This is very good question. So let us let us look at this formula for orthogonal polynomial ensemble as we wrote last time So there we had Regularization this is excellent question. So there we had the formula So there we had the formula So let us recall for orthogonal polynomial ensemble orthogonal polynomial ensemble. We had the formula dp Over dpq Is the weight of the ensemble the weight of the ensemble at P over k and Of wq over kn q q Times this product So this is how the formula looks for the orthogonal polynomial ensemble. So to get the weight one needs to take the limit of these We could take the weight one needs to take the limit of these which is trickier if one has regularization So if one doesn't have regularization it is straightforward It has regularization. It is tricker Okay. Yes, that doesn't make sense. Yes Okay, so Now Let me just say there. So let me introduce the gamma kernel of Brodin and Dalshansky So obtained as limit of that measures about which Pierre spoke to us on Monday and Just discreet kernel on Z So it is again an integrable expression with Gamma functions, so I will write a Z that prime over square root of gum Z plus X that prime effects I write it in this way So that this expression is well defined as we saw in the talk of Pierre either when Z is equal to Z That prime is equal to Z bar or when Z that prime all lie in the same interval M and plus one There is also a discrete series, but let's skip that For the time being by the way what Pierre did not say, but it should be said that The Z measures arise In the representation theory are intimately connected representation theory of SL2R So the terms principle series and complementary series and discrete series these are in fact principle representations of SL2R Complimentary presentation of SL2R and so forth. So and I write So the gamma kernel K Z that prime is the So this is the gamma kernel So and this kernel as I said it it arises from a measure on Partitions so observe that it has integrable form. So by definition The kernel has integrable form it arises from measures on partitions. So it should not very greatly surprise us that There are very few particles on the positive semi-axis and very many particles on the negative semi-axis in such a way that KXX is one over X as X goes to plus infinity and KXX is one minus one over X as X goes to minus infinity. So again, let us recall that we are having Just young diagrams and in young diagrams. There are very many holes very many particles here Okay, as usual I miss. Yes. No. No, I wrote correctly. Excuse me. No, that's quite precise. I wrote correctly. So I have not To my own surprise. I have not confused particles and holes. So, okay Okay, so there are very many holes here very many particles here and so this is the gamma kernel and so clearly This multiplicity function is not defined The regularized multiplicity function, however, is defined and regularization will in this play in this case Regularization will take the following form So regularization regularization will take the following form to regularize the quantity when there are too many particles for things to converge One regularizes it in the following way So zip I Take product of g of X over particles so X bigger than zero and Then I take inverse of Y over holes Why less than zero so here is X in X Why not in X? So on the so in the positive semi-axis, I have very many Particles, excuse me the opposite. I have very few particles. I have very few particles So I can take product over those on The negative semi-axis on the other hand. I have very many holes so I can take product over those in fact when I subtract the exponential so Let me let me formulate it like this when I subtract exponential of the trace I subtract a term corresponding to the set where corresponding to the configuration where all these are particles I subtract all so to speak all the particles So what remains is where I have the holes? So and this is the regularization for the multiplicative functional, and I think I mentioned and Let me say this again I mentioned that this whole subject started from a question of Alshansky in fact Alshansky in 2011 Treated the gamma kernel so Alshansky Treated in 2011 the action of the infinite symmetric group on the gamma kernel on the point process with a gamma kernel And he proved this formula for this specific G. He proved this formula so for this specific case by taking limit transition from young diagrams, so in fact the the Expression this expression can be written down explicitly for young diagrams, so he has that measure one can then write explicitly this product expression and So he wrote this expression, and then he asked me what happens for the same process, and well here is the answer Okay, so here Finishing with the examples, please allow me to pursue a digression So in these two examples so the Bessel kernel and the gamma kernel one sees a One observes a phenomenon for which I would like to have a more Conceptual explanation, so the phenomenon is the follows so the Bessel kernels It's not just it's obviously well a family of Bessel kernels, but in fact it's not just a family It's a hierarchy of Bessel kernels, so let me point out that Js of xy is equal to Is equal to Js Plus two of xy Plus s plus one Square root of x. Let me write it like this s plus one Js plus one square root of x Square root of x j a plus plus one Square root of y square root of y Okay, so Bessel kernel with index s is a rank one perturbation of Bessel kernel with Index s plus two and so here well as speaker I get question But here I would like to ask a question to the experts in the audience so to every such Determinant open process there corresponds a integrable system unless I'm mistaken, so they They determine and as a gap probability the determinant is a solution Solution of some integrable system So my question is what so here I have a hierarchy of kernels What is the corresponding hierarchy on the level of integrable systems? Here's question. Just I would like to ask Okay, so Yes, so observe that they So corollary corollary that the sequence The sequence square root of r Js Excuse me. Yes square root of r Jr of Square root of x over square root of x Forms an orthogonal basis Forms an orthogonal basis An orthogonal orthonormal basis for the range of Js So the convenience of this orthonormal basis is that it's iterative. So it's a basis So our our Takes values. So our takes values s plus one s plus three and so on s plus one s plus three s plus five and so on so but observe that this basis is iterative this basis is iterative so Just if I take s plus two then there is one element less So well and clearly in fact it is also clear from this formula clearly Of course the Bessel kernels they go to zero as s goes to infinity. They will converge to zero. So there is everything is consistent and Let me just say that this This perturbative statement can also be expressed on the level of multiplicity functional So with the after this it should not be very surprising So in fact, I can also have with palm measures. I can also say That palm measure So the palm space. So let me write for this time LS is the range of Js So the palm space of LS LS of P Which is by definition. Excuse me. Let me write it here. So LS of P as always the palm space LS of P the palm space that is to say F in LS F of P equals zero So I can write LS of P is in fact equal to X minus P over X L s plus two So this is formula I can write so in fact, there is a there is a Recurrent this recurrence relation it makes perfect sense in terms of palm Theory so the next vessel kernel is obtained by adding a particle to the to the previous vessel kernel In fact, you can see it's a rank one perturbation It's rank one perturbation. So I add one more particle to the previous vessel kernel. Here it is, right? so that is to say that the palm measure of this one is equivalent to this one Palm measure of this one is equivalent to this one Okay, and so here it can be written explicitly and so then there is a corollary which is published in Proceedings of the Stegloff Institute. So Just the corollary in 2016 the corollary is that well, of course the corresponding measure the palm measure At point P is absolutely continuous with respect to the palm measure Excuse me with respect to the measure with shifted parameter And the radonnik-Oedim derivative is just x minus P over x Square x in x well with some normalization constants that Here it is just normal normal product without any anything so normal product, okay, so this much for the vessel kernel and Let me also very briefly say that the same Result is obtained in recent joint work with Olszanski from 2019 also for the Gamma kernel, so let me let's think that we already remember the regularization the scheme of regularization Okay, I raise this also so for gamma kernel in joint work with Olszanski 2009 it's on the archive Olszanski and 2000 joint work from 2019 so just Same statement for the gamma kernel, so we can have also there is a little nuance here we can have an iterative basis, so let me write it down Is some constant of that that prime which let me not even bother writing down times A x plus Z times gum X plus that's One so I should say in the paper of course with Olszanski. We use the Notation of Olszanski where there are one halves everywhere so everywhere in all the formulas with every integer There is one half one half one half everywhere, so I skip them in this presentation so just There is this basis and then one can write K X Y K. Yes, that's a prime X Y So for the gamma kernel one can write this representation explicitly. It is an inductive representation GM Z that prime Of X GM of Y so so The sum is from emical zero to infinity This gives in turn So this basis is orthogonal basis It's orthogonal basis for Z equals to Z prime bar So in principle series, it's orthogonal basis and this session is completely the same as in the Bessel case It's orthogonal. It's orthogonal basis and so orthogonal inductive basis in Complementary series. It's not orthogonal basis. It's by orthogonal basis. It's not orthogonal is by orthogonal basis Okay, however, this may be one obtains a recurrence relation very similar to the one for Bessel K Z that prime. Okay, let me write it here. I erase the definition of the gamma kernel. We already remember it so let me write it here so the K Z that prime X Y is equal to G zero Of X G zero of Y. Well, obviously that's at prime so and there is there is a Well the next kernel plus K Z plus one that prime plus one but there is a little nuance for the gamma kernel namely there is a shift so there is a shift and a twist a gauge transformation a Z that prime of X a Z plus one that plus plus one of Y Excuse me of X. I wanted to say and the other the same thing of Y a Z plus one that prime plus one of Y a Z that prime of Y So this is just the formula for gamma kernel observe that well it is a little bit twisted this twist is twist by function of episode value one in orthogonal case, but in a non orthogonal case this function is not of absolute value one And also by the way, I take advantage to ask a question to the experts in the audience So what would be the integrable system corresponding to the gamma kernel? What would be just the gap determinant for the gamma kernel? Is it possible to is it possible to write? I don't know pen live a equation which corresponds to it So or is it possible to write? Some how do you say the integral systems that lies behind this kernel? Okay, and in particular so from this hierarchy. We also obtain again that the palm measure the palm measure, so let me just not write the formula Let me refer to the pre to the preprint but again the palm measure the palm measure of gamma kernel measure of the gamma kernel of P K z is Equivalent up to an explicitly written multiplicity functional in fact multiplicity functional is always the same Multiplicate functional is the same just it has to be understood in a regularized sense is equivalent to PK Z plus one z prime plus one so there is the same hierarchy in this Gamma case also and in concluding this digression. Let me put a digression on a digression so Just let me say that with this With this hierarchy it is possible to construct an Analog of Determinantal measures, but which are not finite but sigma finite so and let me let me say this and with this I will finish so it is possible to construct an object which I call infinite determinant measures infinite determinant measures so in fact the need for this object came from the following construction of Bardin and Al Shansky who observed that the best cell kernel the best cell kernel arises in question of Ergodic decomposition of measure on the space of infinite matrices let For lack of time, please allow me to be very brief here So they consider a space of matrix a space of measures on matrices, which I will write now So this is a sequence of measures CN sequence of measures on just space of matrices Complex matrices, so let me point out that These measures are finite when s is bigger than minus one So finite So these measures arise in fact, so if s is equal zero, this is very specific measure This is measure. So what does it mean space of matrices space of matrices? It is in fact complex grass mania. So if you think about it think about complex Think think about manifold CN in C2n. What does it mean manifold of half dimension manifold of half dimension is graph of A map so this graph of a map is precisely a matrix n times n So grass mania so a flat coordinate on grass mania precisely identifies the grass mania With the space of matrices n times n complex matrices n times n complex matrix is identified with grass mania complex grass mania to Nm Up to obviously up to some negligible sets Then the canonical invariant measure on the grass mania is identified with precisely this measure, but with s equals zero So grass mania carries a canonical invariant measure. So it is homogeneous space u n cross u to n Double quotient of unit carries canonical invariant measure. So this canonical invariant measure under passing to the flat coordinate becomes this the canonical invariant measure of the grass mania Totologically is unitary invariant and Totologically projection Totologically if I take grass mania of dimension n plus one and project of grass mania of dimension n the measures the invariant measures We'll also project so one obtains that these measures are also projectively Equivariant the miracle is that the property of projection Equivariant preserves For all s so for this miracle. I don't have convincing explanation. It's possible to write some other measure on grass mania It's possible also to see this in terms of some Gaussian distribution And then somehow instead of Laguerre polynomials with s equals zero consider Laguerre polynomials with well s equal s something like this But I don't have conceptual explanation. Why these measures actually arise So but these measures do arise as this is sequence of measures projectively Projectively equivariant so that is to say for matrix of order n plus one I pass the matrix from order n Then the measures are one measure is taken on to the next measure by the way open question These are the only ones multiplicative in eigenvalues and projectively Equivariant open question. I have no there is some result of this type by Raskowski for That measures but for these measures nothing so open questions these that they are canonical in this sense However, this may be these measures exist on infinite matrices. So they're so this projective family of measures define Define a measure on space of infinite matrices and this measure Decomposing this measure into our godly components gives Bessel process Nonetheless so the it's very nice, but this measure can also be defined when it is infinite So if S is less than minus one The measure is still well defined measure still well defined still well defined measure still well defined so it will be infinite measure, but all Infinity will live only for some small values of n If n is sufficiently large then the fiber so as I mentioned we consider projective family of measures Then the fibers will have actually finite measure So the measure on space of infinite matrices will be well defined So there is question of our godly decomposition and it would have to be infinite measure on space of configurations and in fact Infinite measure on space of configurations can be constructed. So it has been constructed So this was question of Borodin-Alchanski So our answer to this question Borodin-Alchanski can be constructed by iterating this procedure still further It is possible to iterate this procedure still further so to perturbed a Determinant kernel to perturbed a determinant kernel by a non-square integrable function or in other words to consider a measure of which measures are Determinant, but it the measure is sigma finite So in the fact it is possible to check is that perturbing perturbing determinant measure by Non-square integrable function considering perturbation by projection adding an unbounded operator not not perturbing it by rank one operator But perturbing it by unbounded operator Corresponds to adding a particle to my configuration, but this particle So to speak the probabilities of this particle approaches the edge grows and grows and grows and in fact is infinite And so instead of determinant measures one or by the way equivalent way of seeing this infinite determinant measure is the just product of Determinant measure by multiplicative functional which Converges which converges, but is not square integrable. So then the space square root of gl Will no longer be space of integrable functions the space will be well defined But it but the fun so it's quite easy to have some space of in l2 and then multiplied by some function in such a way Is that the space is no longer space of square integrable functions space of functions whose norm is infinite and to such object will correspond analog of determinant measure But which will be infinite which has all the properties of the terminal measures which becomes the terminal measure Undertaming so one can tame in different ways obtain different measures, but the object is one and to such perturbation of To such finite rank perturbation of Hilbert space by non integrable functions one obtain Finite particle perturbation of determinant measure and infinite determinant measure. Thank you very much


Kirby and the Forgotten Land is something bold and new for the famous pink puffball. A full 3D title with a strong focus on exploration, it's decidedly different to the years of side scrollers that have come before. After a period of stagnation, Hal Laboratory and Nintendo have finally given Kirby something new and fresh. There is a good reason, though, why it took so long for Kirby to go fully 3D in a platformer. According to the developers, getting Kirby to work in 3D was actually incredibly difficult. Before we can talk about these challenges, though, we need to first talk about the so-called Lost Kirby games. 3D gameplay isn't the only major challenge that Kirby developers have faced. According to Hal Laboratory General Director Shinya Kumazaki, looking back on the history of the Kirby series, there was a period of time when certain game concepts simply refused to come together. As a result, we weren't able to release a mainline Kirby game on a home console for a little over a decade. We kept hitting walls we couldn't climb over. During this period, Hal started work on multiple Kirby games before ultimately scrapping them. There was a four-player co-op game that was in development at around the time of Kirby's air ride, but the multiplayer aspects proved too challenging. There was also a game described as an animated Kirby, sort of like a pop-up book, with an art style that looked fundamentally different to anything the series had seen before. Most relevant to the Forgotten Land was a scrapped game, which was described by Shigafumi Kawazi. It was an experiment with extremely challenging gameplay that placed Kirby in 3D space and allowed players to move around freely. But unfortunately, we weren't able to achieve the quality we hoped for and it never reached completion. It seems that, during this period, the developers at Hal really weren't sure what they even wanted the Kirby series to be moving forward. The ultimate decision was to abandon 3D altogether for the moment, but the team did slowly iterate and experiment in subsequent games. Said Kumazaki, from that point on, our game prototype shifted to a trial-and-error approach. We played with unconventional gameplay angles through comparatively smaller games in the series as a way to further explore the concept of a Kirby-based 3D platformer. We still had plenty of unique challenges to overcome, though. Some in Hal Laboratory even felt that only 2D games should count as real Kirby games, so to speak. So, we weren't able to reach a point where we could deliver a complete 3D platforming mainline Kirby title. The problem, according to the developers, is that for several reasons, Kirby just doesn't work well in 3D. The most obvious issue is his character design. Because he's a large round blob, no matter which angle he's viewed from, he looks the same. This doesn't make a difference in 2D, but in 3D it becomes very difficult to tell which direction Kirby is facing. The other challenge, somewhat connected, is that the developers wanted to keep any new Kirby game as simple and easy to play as possible. Said Kumazaki, I pictured a 3D platformer easy enough that even a 3-year-old child could play. The main complication in modern gaming that would trip up a 3-year-old is the camera. To make the game as simple and easy as possible, the team needed an intuitive, coordinated computer-controlled camera that prevented the player from getting stuck. This camera also had to mitigate the fact that Kirby's direction is difficult to read in a 3D space, especially when confronting enemies. This 3D environment also meant that it was difficult to tell when Kirby completed his jumps. When jumping immediately after landing on the ground, players would often tap the jump button a second too soon, and Kirby would float rather than launch himself into the air. This is a common problem with 3D platformers, and it feels awful when the character doesn't seem to be responding to the player simply because the player can't tell where the ground is. The solution to both this and the challenge of direction was simply to build the game's mechanics around what the player thinks they see, rather than what is actually happening. For example, if the camera angle suggests that Kirby has successfully hit an enemy, then it counts as a hit, even if, when viewed from a different angle, the attack was aimed in the wrong direction. Similarly, the team implemented what they call fuzzy landing. If the player hits jump before Kirby has quite made it to the ground, it still counts as a jump, rather than an attempt at hovering. This made for a much easier and less frustrating gameplay experience. The problem? Now the game was too easy. When staff at Nintendo played early versions of The Forgotten Land, the games felt sparse. There weren't enough enemies to actually make the game feel interesting. At one point, Nintendo producer Kaininomiya asked plainly, why aren't the stages more densely populated? According to Kumazaki, everyone on our development staff really loves Kirby, so no one wanted to torment him with an unfair situation. Nino-miya responded, the 3D gameplay didn't have as much bite at first, but I never would have guessed that could be sourced back to the development team wanting to protect poor Kirby. Of course, the other issue was that the team didn't want to overwhelm inexperienced players with too many challenges. The game shouldn't feel too stressful. With a 3D space, though, it was simple for players to negotiate their way past a lot of enemies in a way that wouldn't be possible in 2D. Reluctantly, the team at HAL increased the number of obstacles in their levels to better suit the 3D space. While 3D may have been a headache for Kirby developers, it also provided an opportunity, said Kumazaki. Near the beginning of development, we spent a lot of time discussing the kinds of movement and visuals we could add that might feel unique to Kirby, ones that you wouldn't find in other 3D platformers. Then we thought about Kirby's unique characteristics and realised that, to make a truly great 3D platformer, we should embrace his innate humour. He's this funny little puffball, always changing shapes, squashing and stretching as he gobbles up everything around him. This then informed Kirby's new mouthful mode, making use of the 3D space to transform Kirby into a variety of different 3D shapes that would never have worked in a side-scrolling game. The result is a Kirby game unlike anything that has come before, a big leap into a new direction for the series. The moral of the story is that just because a challenge is hard, it doesn't mean that it's impossible. Faced with the challenge of rethinking Kirby gameplay for three dimensions, some at HAL laboratory simply felt that it couldn't be done. It didn't fit the character. However, after a lot of trial and error, the team were able to solve the big challenges that made a 3D Kirby seem impossible. Similarly, you will meet challenges in life that seem insurmountable. You may get discouraged, thinking you'll never be able to learn a new skill or achieve a goal. If you keep trying, though, experimenting and exploring your own abilities, and if you're not afraid of failing multiple times along the way, you can transform an impossible task into a fantastic achievement.


The other state government has accused the immediate past national chairman of the All Progressive Congress, APC, and the former governor of the state, Adamso Schoenmele, of being the mastermind of the protests that broke out in Benin City on Wednesday, which claimed three lives and saw the destruction of some banks. The protestors had expressed anger over the scarcity of the new marinades. The state government, which described the riots as systematic and targeted at the PDP-controlled states, called on security agencies to arrest Schoenmele. We believe that the incident of yesterday had a certain purpose. It's, as you can see, as we've said in the press conferences today, it didn't happen by accident. We know that towards elections like this, the practice by the opposition party is to create disenchantment. During my last election, you know how many markets they vote. So this is the same trend. This is what they are trying to achieve in a day to create chaos, to create disaffection in the minds of the people. Unfortunately, as though we have it, we are opposition party at the national level. We're not the one that created these policies.  In a swift reaction, however, Schoenmele distanced himself from the riots and asked the state government to look elsewhere. It's a late blames for its poor performance in the state.