Department of Mathematics

West Chester University

Mathematics Information
Office: Room 101
25 University Avenue
West Chester, PA 19383
Phone (610) 436-2440
Fax (610) 738-0578
Email: Department Chair

Title: Decay of correlations for Lorentz gases

Abstract: The planar periodic Lorentz gas is a deterministic model for stochasticity. In particular, it is known that the motion of almost every gas molecule is asymptotically like a sample path for planar Brownian motion. Less well-understood is the decay of correlation (loss of memory/gain of statistical independence) for such systems.

In this talk, I will describe recent, and in some cases on-going, results on decay of correlations for various continuous time Lorentz gas models, including (in)finite horizon Lorentz gases, Bunimovich stadia, and cuspoidal domains.

In particular, a recent result proves that the classical infinite horizon Lorentz gas with a doubly periodic array of circular scatterers has decay of correlation rate 1/t as anticipated by physicists.