{
  "id": "math/0405157",
  "version": "v2",
  "published": "2004-05-10T00:50:31.000Z",
  "updated": "2006-07-12T10:31:16.000Z",
  "title": "The mixing time for simple exclusion",
  "authors": [
    "Ben Morris"
  ],
  "comment": "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)",
  "journal": "Annals of Applied Probability 2006, Vol. 16, No. 2, 615-635",
  "doi": "10.1214/105051605000000728",
  "categories": [
    "math.PR",
    "math-ph",
    "math.MP"
  ],
  "abstract": "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.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2006-07-12T10:31:16.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60J05"
    ],
    "keywords": [
      "mixing time",
      "simple exclusion",
      "auxiliary markov chain",
      "relaxation time",
      "exclusion process"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2004math......5157M"
    }
  }
}