Lorentz gas with small scatterers; some non-standard Limit Theorems

Vienna Probability Seminar

A main theme in smooth ergodic theory is to explain and rigorously prove the occurrence of statistical laws for deterministic dynamical systems. If an invariant measures is taken to consider a dynamical system as stochastic process, then this process is at best highly dependent.
Lorentz gas is a model of uniform movement with elastic collisions on a grid of convex scatterers, used to describe the motion of electrons in a metal. In this talk, I want to discuss some limit theorems (non-standard Gaussian, local limit) that can be proven when not only times goes to infinity, but also the scatterer size goes to zero.