Cluster expansion for a dilute hard sphere gas dynamics

TL;DR

This paper introduces a new approach to analyze dilute hard sphere gas dynamics by applying cluster expansion directly to particle trajectories, providing insights into fluctuations and clustering behavior beyond traditional methods.

Contribution

It presents an alternative cluster expansion method on real trajectories, offering a new perspective and recovering previous results while describing particle clustering.

Findings

Recovered fluctuation and large deviation results

Provided a detailed description of particle trajectory clustering

Offered a novel direct trajectory-based analysis method

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.