Workshop
A quantitative central limit theorem for the simple symmetric exclusion process
- Vitalii Konarovskyi
Abstract
We prove a quantitative central limit theorem for the simple symmetric exclusion process (SSEP) on a multidimensional discrete torus in local equilibrium. Our main result establishes the optimal rate of convergence of the density fluctuation field to the generalized Ornstein–Uhlenbeck process.
The proof is based on a detailed comparison of the generators of the SSEP fluctuation field and the limiting Ornstein–Uhlenbeck dynamics. The main ingredients are a careful control of the resulting error terms, regularity properties of the Ornstein–Uhlenbeck semigroup, and an infinite-dimensional Berry–Esseen bound for the initial particle fluctuations.
This is joint work with Benjamin Gess.
