A quantitative central limit theorem for the simple symmetric exclusion process

2024/08/02 by Benjamin Gess, Gess, Benjamin, Vitalii Konarovskyi +1 · 1 citation
Mathematics · Physics and Astronomy · #60F05 #60H15 #60J25 #60K35 #Advanced Thermodynamics and Statistical Mechanics #FOS: Mathematics #Probability (math.PR) #Random Matrices and Applications #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.2408.01238

openalex publication_date 2024/08/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

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.

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