Billiards correlation functions

We discuss various experiments on the time decay of velocity autocorrelation functions in billiards. We perform new experiments and find results which are compatible with an exponential mixing hypothesis first put forward by Friedman and Martin (FM): they do not seem compatible with the stretched exponentials believed, in spite of FM and more recently of Chernov, to describe the mixing. The analysis leads to several byproducts: we obtain information about the normal diffusive nature of the motion and we consider the probability distribution of the number of collisions in timet_m (ast_m), finding a strong dependence on some geometric characteristics of the locus of the billiard obstacles.This paper is dedicated to Philippe Choquard on his 65th birthday