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.