Long-time derivation at equilibrium of the fluctuating Boltzmann equation

TL;DR

This paper proves that for a hard sphere gas at equilibrium, the fluctuations converge to a Gaussian process described by the fluctuating Boltzmann equation over arbitrarily long times in the low density limit.

Contribution

It extends the understanding of fluctuation convergence to the fluctuating Boltzmann equation for long times at equilibrium in a low density gas.

Findings

Fluctuations converge to a Gaussian process.

Convergence holds for arbitrarily long times.

Method improves upon previous weak convergence techniques.

Abstract

We study a hard sphere gas at equilibrium, and prove that in the low density limit, the fluctuations converge to a Gaussian process governed by the fluctuating Boltzmann equation. This result holds for arbitrarily long times. The method of proof builds upon the weak convergence method introduced in the companion paper [8] which is improved by considering clusters of pseudo-trajectories as in [7].