Lecture: Randomness, continuum and complex analysis

Wendelin Werner


The fact that space and time can be continuous is rather intuitive. But when one thinks of random phenomena, the natural examples that first come to mind are of discrete nature, such as coin tossing.
The conceptual question on how randomness can be split up into and reassembled from infinitesimal little pieces turns out to be quite tricky and related to several different fields of mathematics, as well as mathematical physics (in particular for the study of phase transitions, sometimes referred to as critical phenomena) or theoretical computer science. It is related to contemporary research in mathematics that we shall illustrate via some concrete examples.