Georgia Institute of Technology College of Sciences

Mark Kac proposed in 1956 a program for deriving the spatially homogeneous Boltzmann equation from a many-particle jump collision process. The goal was to justify in this context the molecular chaos, as well as the H-theorem on the relaxation to equilibrium. We give answers to several questions of Kac concerning the connexion between dissipativity of the many-particle process and the limit equation; we prove relaxation rates independent of the number of particles as well as the propagation of entropic chaos. This crucially relies on a new method for obtaining quantitative uniform in time estimates of propagation of chaos. This is a joint work with S. Mischler.