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Cluster expansion for a dilute hard sphere gas dynamics

Abstract : In [7], a cluster expansion method has been developed to study the fluctuations of the hard sphere dynamics around the Boltzmann equation. This method provides a precise control on the exponential moments of the empirical measure, from which the fluctuating Boltzmann equation and large deviation estimates have been deduced. The cluster expansion in [7] was implemented at the level of the BBGKY hierarchy, which is a standard tool to investigate the deterministic dynamics [11]. In this paper, we introduce an alternative approach, in which the cluster expansion is applied directly on real trajectories of the particle system. This offers a fresh perspective on the study of the hard sphere dynamics in the low density limit, allowing to recover the results obtained in [7], and also to describe the actual clustering of particle trajectories.
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https://hal.archives-ouvertes.fr/hal-03661646
Contributor : Sergio Simonella Connect in order to contact the contributor
Submitted on : Saturday, May 7, 2022 - 11:27:39 AM
Last modification on : Tuesday, May 10, 2022 - 3:47:02 AM

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  • HAL Id : hal-03661646, version 1
  • ARXIV : 2205.04110

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Thierry Bodineau, Isabelle Gallagher, Laure Saint-Raymond, Sergio Simonella. Cluster expansion for a dilute hard sphere gas dynamics. Proceedings of the International Congress on Mathematical Physics, special issue of Journal of Mathematical Physics, In press. ⟨hal-03661646⟩

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