First quantitative convergence rate for mean-field fluctuation processes: 1/√N for regular drifts, with weaker rates for singular vortex and Coulomb kernels.
A quantitative central limit theorem for the simple symmetric exclusion process
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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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Convergence rate for Fluctuations of mean field interacting diffusion and application to 2D viscous Vortex model and Coulomb potential
First quantitative convergence rate for mean-field fluctuation processes: 1/√N for regular drifts, with weaker rates for singular vortex and Coulomb kernels.