Thierry Bodineau (Ecole Polytechnique)

Statistical description of hard sphere gas dynamics

Abstract: Since the seminal work of Lanford, the convergence of the hard-sphere dynamics towards the Boltzmann equation has been established in a dilute gas asymptotic. The main feature of this kinetic limit is the emergence of the irreversibility in the limit, instead the microscopic dynamics is reversible. We are going to discuss the fluctuations around the Boltzmann equation and the convergence of the fluctuation field to a generalized Ornstein-Uhlenbeck process. This analysis relies on the study of the correlations created by the Hamiltonian dynamics. We will see that the emergence of the irreversibility in the kinetic limit can be related to the singularity of these correlations. If time allows, we will also discuss the large deviations for the hard-sphere dynamics.