A quantitative central limit theorem for the simple symmetric exclusion process

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.