We show that for the mean zero simple exclusion process in ℤd and for the asymmetric simple exclusion process in ℤd 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.
Milton Jara. "Finite-dimensional approximation for the diffusion coefficient in the simple exclusion process." Ann. Probab. 34 (6) 2365 - 2381, November 2006. https://doi.org/10.1214/009117906000000449