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

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

2005-11-10

arxiv.org/abs/math/0511249v2

Annals of Probability 2006, Vol. 34, No. 6, 2365-2381

Mathematics

Probability

Published at http://dx.doi.org/10.1214/009117906000000449 in the Annals of Probability (http://www.imstat.org/aop/) by the Ins

Scientific paper

10.1214/009117906000000449

We 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.

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