Scaling limits in Kinetic theory
Summer School - Lyon - 2019

Minicourse by Thierry Bodineau (École Polytechnique, Paris)
and by Isabelle Gallagher (ENS, Paris)

Statistical description of a hard sphere gas dynamics : fluctuations and large deviations

The goal of this minicourse is first to present Lanford's derivation of the Boltzmann equation starting from a deterministic system of hard spheres satisfying Newton's laws with elastic collisions. Next, we shall see that this limiting process can be understood as a Law of Large Numbers, and we shall further explore the behaviour of fluctuations, proving in particular a Central Limit Theorem. Finally we shall discuss a Large Deviation Principle.