The mixing time for simple exclusion
| dc.creator | Morris, Ben | |
| dc.date | 2004-05-10 | |
| dc.date | 2006-07-12 | |
| dc.date.accessioned | 2026-07-07T06:36:46Z | |
| dc.date.available | 2026-07-07T06:36:46Z | |
| dc.description | 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. | |
| dc.description | Published at http://dx.doi.org/10.1214/105051605000000728 in the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org) | |
| dc.identifier | https://arxiv.org/abs/math/0405157 | |
| dc.identifier | http://arxiv.org/abs/math/0405157 | |
| dc.identifier | Annals of Applied Probability 2006, Vol. 16, No. 2, 615-635 | |
| dc.identifier | doi:10.1214/105051605000000728 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/100191 | |
| dc.subject | Probability | |
| dc.subject | Mathematical Physics | |
| dc.subject | 60J05 (Primary) | |
| dc.title | The mixing time for simple exclusion | |
| dc.type | text |