Quantitative ergodicity for the symmetric exclusion process with stationary initial data

Abstract

We consider the symmetric exclusion process on the d-dimensional lattice with initial data invariant with respect to space shifts and ergodic. 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 $\overline{d}$-distance. The proof is based on the analysis of a two species exclusion process with annihilation.