The planar periodic Lorentz gas model was introduced in the 1905 as a deterministic model for Brownian motion. (This was made precise by M. Nicol and the speaker in 2007.) Nowadays, Lorentz gases retain their interest for Mathematical Physics, but also provide an important class of examples in smooth ergodic theory, where the aim is to understand dynamical systems from a probabilistic viewpoint.

Decay of correlations measures the rate of mixing, or loss of memory, in a deterministic system. Mixing for flows (continuous time dynamical systems) is an important and much studied, but still poorly understood, problem. This talk will focus on recent progress for a class of (nonuniformly hyperbolic) dynamical systems which includes many of the classical examples such as Henon and Lorenz attractors as well as Lorentz gases.