Statistical properties of a hard sphere gas
A gas dynamics can be modeled by a billiard of hard spheres, moving according to the laws of classical mechanics. Initially the spheres are randomly distributed according to a probability measure which is then transported by the deterministic flow of the Hamiltonian dynamics. Since the seminal work of Lanford, it is known that the gas density converges, in the low density limit, towards a solution of the Boltzmann equation. We are going to review several results on the fluctuations of the hard sphere gas density around the Boltzmann equation as well as on the large deviations away from the typical behavior. This talk is based on joint works with I. Gallagher, L. Saint-Raymond, S. Simonella.