LONG-TIME DERIVATION AT EQUILIBRIUM OF THE FLUCTUATING BOLTZMANN EQUATION

• 成果类型: Article
• 署名作者: Bodineau, Thierry; Gallagher, Isabelle; Saint-raymond, Laure; Simonella, Sergio
• 署名单位: Universite Paris Saclay; Centre National de la Recherche Scientifique (CNRS); Centre National de la Recherche Scientifique (CNRS); Universite PSL; Ecole Normale Superieure (ENS); Sapienza University Rome
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/23-AOP1656
• 发表日期: 2024
• 页码: 217-295
• 关键词: rarefied-gas

摘要

We study the deterministic evolution of a gas of hard spheres, initially distributed according to the equilibrium measure, and prove that, in the lowdensity limit, the fluctuation field converges to a Gaussian process governed by the fluctuating Boltzmann equation. This result holds for arbitrarily long times.