The Annals of Probability· 2026Q1
A quantitative central limit theorem for the simple symmetric exclusion process
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- 2026year
Short summary
A quantitative central limit theorem for the simple symmetric exclusion process (SSEP) on a d-dimensional discrete torus is proven, establishing an optimal rate of convergence.
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Key points
- A quantitative central limit theorem is established for the simple symmetric exclusion process (SSEP) on a d-dimensional discrete torus.
- The proof involves comparing SSEP generators with a generalized Ornstein–Uhlenbeck process.
- An infinite-dimensional Berry–Essen bound is used for initial particle fluctuations.
- The derived rate of convergence for the SSEP's fluctuations is shown to be optimal.
AI-generated from the title and abstract; the full text is not read.
Abstract
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.
The authors' abstract, as published at the source. The Annals of Probability, 2026 · DOI ↗
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Field: Mathematical Physics
Mathematical PhysicsMathematics