2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/124811We show that for the mean zero simple exclusion process in $\mathbb {Z}^d$ and for the asymmetric simple exclusion process in $\mathbb{Z}^d$ for $d\geq3$, 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.Published at http://dx.doi.org/10.1214/009117906000000449 in the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org)Probability60K35 (Primary)text