Geometry & Topology Seminar: "Stationary States and Transport in Random Billiard Models"

Abstract: In the theory of Markov chains, a principal concern is the existence and uniqueness of and rate of convergence to stationary measures. We discuss these issues as they relate to a class of Markov chains, which we call random billiards, derived from both standard billiard systems and billiard systems in the presence of an external force field.  For those Markov chains which have a unique stationary measure that is converged to fast enough, properly scaled partial sums of functionals of the Markov chain converge to a Gaussian random variable-- a form of the classical central limit theorem of probability theory.  We discuss techniques for computing statistics of the limit Gaussian with an eye toward understanding their dependence on properties of the underlying billiard systems.

 

Organizer: Xiang Tang