Fluctuating Boltzmann equation and large deviations for a hard sphere gas

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. In this talk, we are going to discuss the fluctuations of this microscopic dynamics around the Boltzmann equation and the convergence of the fluctuation field to a generalised Ornstein-Uhlenbeck process. We will show also that the occurrence of atypical evolutions can be quantified by a large deviation principle. This analysis relies on the study of the correlations created by the Hamiltonian dynamics. We will see that the emergence of irreversibility in the kinetic limit can be related to the singularity of these correlations.

dynamical systemsprobability

Audience: researchers in the topic

( slides | video )

Horowitz seminar on probability, ergodic theory and dynamical systems