Work

A quantitative central limit theorem for the simple symmetric exclusion process

Year: 2026

Type: article

Abstract: A quantitative central limit theorem for the simple symmetric exclusion process (SSEP) on the d-dimensional discrete torus is proven. The argument is based on the 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. In turn, this relies on regularity estimates for the Ornstein–Uhlenbeck process, and higher-order correlations of the SSEP. The obtained rate of convergence is optimal.

Source: The Annals of Probability

DOI: 10.1214/26-aop1844

Authors: Benjamin Gess, Vitalii Konarovskyi

Institution: Technische Universität Berlin

Language: English

Topic: Stochastic processes and statistical mechanics

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: European Commission, Deutsche Forschungsgemeinschaft, Max-Planck-Gesellschaft, Max-Planck-Institut für Mathematik in den Naturwissenschaften

Awards: G1288578048, G5259294090, G8201362140, SFB 1283: Unsicherheit beherrschen und Zufall sowie Unordnung nutzen in Analysis, Stochastik und deren Anwendungen