A quantitative central limit theorem for the simple symmetric exclusion process

TL;DR

This paper proves a quantitative central limit theorem for the simple symmetric exclusion process on a discrete torus, establishing optimal convergence rates by comparing generators and using Berry-Essen bounds.

Contribution

It introduces a novel approach to quantify the convergence rate of the SSEP to a Gaussian process, improving upon previous qualitative results.

Findings

Optimal rate of convergence established

Generator comparison technique developed

Berry-Essen bounds applied in infinite dimensions

Abstract

A quantitative central limit theorem for the simple symmetric exclusion process (SSEP) on a $d$-dimensional discrete torus is proven. The argument is based on a comparison of the generators of the density fluctuation field of the SSEP and the generalized Ornstein-Uhlenbeck process, as well as on an infinite-dimensional Berry-Essen bound for the initial particle fluctuations. The obtained rate of convergence is optimal.