An "Informative" Tour through parts of Probability-nadu
Prof. Mokshay Madiman
Yale University, U.S.A.
We will informally review several interesting results in probability theory that are illuminated by information-theoretic ideas. Our primary focus will be to outline why the central limit theorem can be interpreted as a formulation of the second law of thermodynamics. While doing so, we will indicate why the Gaussian distribution comes with a "logarithmic Sobolev inequality", and what this has to do with concentration of measure and with the Ornstein-Uhlenbeck stochastic process. We will also point out connections to Hilbert space theory, to uncertainty principles, and to the Brunn-Minkowski inequality in convex geometry. The talk, which will touch upon work of Shannon, Stam, Barron and many others, is meant to provide a birds-eye view of some beautiful ideas in probability theory.