Finite-dimensional approximation of the self-diffusion coefficient for the exclusion process

Abstract

We show that for the symmetric simple exclusion process on $/mathbb{Z}^d$ the self-diffusion coefficient of a tagged particle is stable when approximated by simple exclusion processes on large periodic lattices. The proof depends on a similar stability property of the asymptotic variance of additive functionals of mean 0. This requires establishing a property for the Dirichlet space known as the Liouville-D property.