{
  "id": "1108.1708",
  "version": "v2",
  "published": "2011-08-08T13:50:42.000Z",
  "updated": "2012-06-06T21:17:47.000Z",
  "title": "Mixing and hitting times for finite Markov chains",
  "authors": [
    "Roberto Imbuzeiro Oliveira"
  ],
  "comment": "v2 has 18 pages. In revision for EJP",
  "journal": "Electronic Journal of Probability, vol. 7, article 70 (2012)",
  "doi": "10.1214/EJP.v17-2274",
  "categories": [
    "math.PR"
  ],
  "abstract": "Let 0<\\alpha<1/2. We show that the mixing time of a continuous-time reversible Markov chain on a finite state space is about as large as the largest expected hitting time of a subset of stationary measure at least \\alpha of the state space. Suitably modified results hold in discrete time and/or without the reversibility assumption. The key technical tool is a construction of a random set A such that the hitting time of A is both light-tailed and a stationary time for the chain. We note that essentially the same results were obtained independently by Peres and Sousi [arXiv:1108.0133].",
  "revisions": [
    {
      "version": "v2",
      "updated": "2012-06-06T21:17:47.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60J10",
      "60J27"
    ],
    "keywords": [
      "finite markov chains",
      "continuous-time reversible markov chain",
      "finite state space",
      "suitably modified results hold",
      "largest expected hitting time"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 18,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1108.1708I"
    }
  }
}