English

Cluster expansion for a dilute hard sphere gas dynamics

Analysis of PDEs 2022-07-20 v1 Mathematical Physics math.MP Probability

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.

Keywords

Cite

@article{arxiv.2205.04110,
  title  = {Cluster expansion for a dilute hard sphere gas dynamics},
  author = {Thierry Bodineau and Isabelle Gallagher and Laure Saint-Raymond and Sergio Simonella},
  journal= {arXiv preprint arXiv:2205.04110},
  year   = {2022}
}
R2 v1 2026-06-24T11:11:09.555Z