On the derivation of the Boltzmann equation: fluctuations and large deviations

It has been known since Lanford’s result in 1974 that in the limit when the number of particles goes to infinity in a rarefied gas, the one-particle distribution satisfies the Boltzmann equation, at least for a short time. In this talk we shall analyze the fluctuations, and large deviations around that limit. This corresponds to joint works with Thierry Bodineau, Laure Saint-Raymond and Sergio Simonella.