The mixing time for simple exclusion

Details The mixing time for simple exclusion The mixing time for simple exclusion

2004-05-10

arxiv.org/abs/math/0405157v2

Annals of Applied Probability 2006, Vol. 16, No. 2, 615-635

Mathematics

Probability

Published at http://dx.doi.org/10.1214/105051605000000728 in the Annals of Applied Probability (http://www.imstat.org/aap/) by

Scientific paper

10.1214/105051605000000728

We obtain a tight bound of $O(L^2\log k)$ for the mixing time of the exclusion process in $\mathbf{Z}^d/L\mathbf{Z}^d$ with $k\leq{1/2}L^d$ particles. Previously the best bound, based on the log Sobolev constant determined by Yau, was not tight for small $k$. When dependence on the dimension $d$ is considered, our bounds are an improvement for all $k$. We also get bounds for the relaxation time that are lower order in $d$ than previous estimates: our bound of $O(L^2\log d)$ improves on the earlier bound $O(L^2d)$ obtained by Quastel. Our proof is based on an auxiliary Markov chain we call the chameleon process, which may be of independent interest.

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