From hyperbolic billiards to statistical physics

Consider a point particle flying freely on the torus and elastically bouncing back from the boundary of fixed smooth convex obstacles. This is the celebrated Sinai billiard, a rare example of a deterministic dynamical system where rigorous results relevant for statistical physics are available. In this talk, we will briefly review the classical theory (ergodicity, mixing, central limit theorem by Sinai, Bunimovich, Chernov, etc.). Then we will discuss some more recent results, such as the mixing local limit theorem and nonequilibrium density profiles in large domains (based on joint work with D. Dolgopyat and T. Teolis). Finally, we will mention some attempts at studying rarely interacting particles.