Quantitative ergodicity for the symmetric exclusion process with stationary initial data

TL;DR

This paper provides a quantitative analysis of how quickly the symmetric exclusion process converges to its equilibrium distribution, assuming certain initial correlation decay, using a novel approach involving a two-species process.

Contribution

It introduces explicit bounds on the convergence rate of the symmetric exclusion process under ergodic initial data with decay of correlations.

Findings

Explicit bounds on Ornstein ar d-distance convergence

Convergence rate depends on initial correlation decay

Analysis based on a two-species exclusion process with annihilation

Abstract

We consider the symmetric exclusion process on the $d$-dimensional lattice with translational invariant and ergodic initial data. It is then known that as $t$ diverges the distribution of the process at time $t$ converges to a Bernoulli product measure. Assuming a summable decay of correlations of the initial data, we prove a quantitative version of this convergence by obtaining an explicit bound on the Ornstein $\bar d$-distance. The proof is based on the analysis of a two species exclusion process with annihilation.