{
  "id": "1104.0434",
  "version": "v1",
  "published": "2011-04-03T22:48:42.000Z",
  "updated": "2011-04-03T22:48:42.000Z",
  "title": "A sharp estimate for cover times on binary trees",
  "authors": [
    "Jian Ding",
    "Ofer Zeitouni"
  ],
  "comment": "14 pages, no figure",
  "categories": [
    "math.PR"
  ],
  "abstract": "We compute the second order correction for the cover time of the binary tree of depth $n$ by (continuous-time) random walk, and show that with probability approaching 1 as $n$ increases, $\\sqrt{\\tau_{\\mathrm{cov}}}=\\sqrt{|E|}[\\sqrt{2\\log 2}\\cdot n - {\\log n}/{\\sqrt{2\\log 2}} + O((\\log\\logn)^8]$, thus showing that the second order correction differs from the corresponding one for the maximum of the Gaussian free field on the tree.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2011-04-03T22:48:42.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60J10",
      "60G60",
      "60G15"
    ],
    "keywords": [
      "cover time",
      "binary tree",
      "sharp estimate",
      "second order correction differs",
      "gaussian free field"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1104.0434D"
    }
  }
}