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Title: Probabilistic aspects of deterministic Lorentz gas models

Abstract

In this talk, I will survey some recent results on probabilistic
properties of the planar periodic Lorentz gas, which can be viewed as a
simple deterministic model for Brownian motion.

The two main themes are (a) decay of correlations, namely the rate at
which the gas mixes; (b) statistical limit laws such as the central
limit theorem, the law of the iterated logarithm, and convergence to
Brownian motion.

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