## The Annals of Probability

### 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.

#### Article information

Source
Ann. Probab. Volume 30, Number 2 (2002), 483-508.

Dates
First available in Project Euclid: 7 June 2002

https://projecteuclid.org/euclid.aop/1023481000

Digital Object Identifier
doi:10.1214/aop/1023481000

Mathematical Reviews number (MathSciNet)
MR1905849

Zentralblatt MATH identifier
1018.60097

#### Citation

Landim, C.; Olla, S.; Varadhan, R. S. Finite-dimensional approximation of the self-diffusion coefficient for the exclusion process. Ann. Probab. 30 (2002), no. 2, 483--508. doi:10.1214/aop/1023481000. https://projecteuclid.org/euclid.aop/1023481000

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• NEW YORK, NEW YORK 10012 E-MAIL: varadhan@cims.nyu.edu