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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Gess et al. (2024) studied this question.
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