Given this function as input, the Loewner equation gives the family of random planar curves known as the Schramm-Loewner evolution.
Given this function as input, the Loewner equation gives the family of random planar curves known as the Schramm-Loewner evolution. Paul Levy constructed this as the uniform limit of a series of successive approximations which interpolate linearly between random variables on the dyadic rationals, so that the joint distribution at each stage is the same as in the limit. As a random process in the plane it is nowhere differentiable almost surely, and its boundary has fractal dimension 4/3. It itself has dimension 2, the same as a space-filling curve or random walk.  It is defined as an almost surely continuous stochastic process with independent increments normally distributed with expectation zero and variance h given time interval h. For 10 points, name this process, also termed a Wiener process, used to model stock market prices in the Black-Scholes model as well as the diffusion of particles in a fluid.
Given this function as input, the Loewner equation gives the family of random planar curves known as the Schramm-Loewner evolution.
{Brownian motion} (accept {Wiener process} before mentioned)