Keller Colloquium in Computing and Mathematical Sciences
It is a remarkably general fact that very high-dimensional random systems behave in an essentially predictable way. This phenomenon, called concentration of measure, is fundamental both to our everyday experience and as a crucial tool in many problems of contemporary applied mathematics. This talk is not about such applications, but rather about the foundations of the subject. I will explain an approach to this area that is not commonly found in modern references, but that is particularly explanatory and has recently led to the discovery of new concentration phenomena. Along the way we will encounter, among other attractions: (1) Greek goddesses; (2) some unusually shaped soap bubbles; (3) nonlinear control theory! I will not assume any background beyond the most basic notions of probability (variance, Gaussian random variables) and applied mathematics.