Large time fluctuations for a hard sphere gas at equilibrium in the low density regime

Large time fluctuations for a hard sphere gas at equilibrium in the low density regime

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Isabelle Gallagher, Ecole Normale Supérieure de Paris

I will present a recent work, joint with Thierry Bodineau, Laure Saint-Raymond and Sergio Simonella, in which we study a hard sphere gas at equilibrium. We prove that  in the low density limit, the fluctuations converge to a Gaussian process  governed by the fluctuating Boltzmann equation. This result holds for arbitrarily long times. The method of proof builds upon the duality method introduced in in a previous work, which is improved by considering clusters of real trajectories, and no longer pseudo-trajectories associated with a Duhamel iteration.