Finite-dimensional approximation for the diffusion coefficient in the simple exclusion process

Abstract

We show that for the mean zero simple exclusion process in ℤ^d and for the asymmetric simple exclusion process in ℤ^d for d≥3, 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 Sobolev inner product associated with the operator.