Abstract
We study the deterministic evolution of a gas of hard spheres, initially distributed according to the equilibrium measure, and prove that, in the low-density limit, the fluctuation field converges to a Gaussian process governed by the fluctuating Boltzmann equation. This result holds for arbitrarily long times.
Funding Statement
IG and LSR acknowledge the support of a grant from the Simons Foundation MPS No651463-Wave Turbulence.
Acknowledgments
We thank warmly the referees for a careful reading of the manuscript and many useful suggestions.
Citation
Thierry Bodineau. Isabelle Gallagher. Laure Saint-Raymond. Sergio Simonella. "Long-time derivation at equilibrium of the fluctuating Boltzmann equation." Ann. Probab. 52 (1) 217 - 295, January 2024. https://doi.org/10.1214/23-AOP1656
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