Isabelle Gallagher

École Normale Supérieure

From Newton to Boltzmann, fluctuations and large deviations

I will report on a recent works, joint with Th. Bodineau, L. Saint-Raymond and S. Simonella, in which we develop a rigorous theory of macroscopic fluctuations for a hard sphere gas outside thermal equilibrium, in the Boltzmann–Grad limit : in particular we study deviations from the Boltzmann equation (describing the asymptotic dynamics of the empirical density) and provide, for short kinetic times, both a central limit theorem and large deviation bounds.