{
  "id": "1407.7617",
  "version": "v1",
  "published": "2014-07-29T02:31:07.000Z",
  "updated": "2014-07-29T02:31:07.000Z",
  "title": "Exponential concentration of cover times",
  "authors": [
    "Alex Zhai"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "We prove an exponential concentration bound for cover times of general graphs in terms of the Gaussian free field, extending the work of Ding-Lee-Peres and Ding. The estimate is asymptotically sharp as the ratio of hitting time to cover time goes to zero. The bounds are obtained by showing a stochastic domination in the generalized second Ray-Knight theorem, which was shown to imply exponential concentration of cover times by Ding. This stochastic domination result appeared earlier in a preprint of Lupu, but the connection to cover times was not mentioned.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-07-29T02:31:07.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "cover time",
      "stochastic domination result appeared earlier",
      "gaussian free field",
      "exponential concentration bound",
      "generalized second ray-knight theorem"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1407.7617Z"
    }
  }
}