A quantitative central limit theorem for the simple symmetric exclusion process

Benjamin Gess; Vitalii Konarovskyi

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arXiv · 2408.01238

A quantitative central limit theorem for the simple symmetric exclusion process

Benjamin Gess·Vitalii Konarovskyi

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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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Benjamin Gess, Vitalii Konarovskyi. 2024-08-02. A quantitative central limit theorem for the simple symmetric exclusion process. https://arxiv.org/abs/2408.01238

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