We consider a gas of N particles in a box of dimension 3, interacting pairwise with a potential α V(r/ε). We want to understand the behavior of the system in the limit N → ∞, with a suitable scaling for α and ε. If we choose ε = 1, α = 1/N, it is the mean field limit: particles interact weakly at long distance. We are interested in the low density limit ε = N -1/2, α = 1. Then the distance crossed by a particle is constant. This limit is well understood since the work of Lanford: the empirical law of the system converges to a solution of the Boltzmann equation. It is a kind of Law of Large Numbers. Sadly this convergence occurs only for a short time. In order to go to longer times, we study the fluctuations around the equilibrium, which follow a linearized version of the Boltzmann equation. The talk will present the idea of the proof of Bodineau, Gallagher, Saint Raymond and Simonella for hard sphere potentials and the idea of an improvement in case of realistic interaction potentials.