# On the derivation of the Boltzmann equation : irreversibility and fluctuations

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 try to justify the appearance of irreversibility in the process, and analyze the fluctuations around that limit. This corresponds to joint works with Thierry Bodineau, Laure Saint-Raymond and Sergio Simonella.