DIFFUSION-APPROXIMATION FOR BILLIARDS WITH TOTALLY ACCOMMODATING SCATTERERS

We study the 2D motion of independent point particles colliding with a periodic array of circular obstacles. The interaction between the par ticles and the obstacles is described by a total accommodation reflect ion law. Assuming that the array of scatterers has finite horizon, the density of particles is approximated by the solution of a diffusion e quation in the long-time and large-scale regime. The proof relies on a multiscale asymptotics and gives the order of approximation.