{
  "id": "1110.3367",
  "version": "v2",
  "published": "2011-10-15T00:22:26.000Z",
  "updated": "2012-06-05T21:06:25.000Z",
  "title": "On cover times for 2D lattices",
  "authors": [
    "Jian Ding"
  ],
  "comment": "21 pages, major revision upon previous version",
  "categories": [
    "math.PR"
  ],
  "abstract": "We study the cover time $\\tau_{\\mathrm{cov}}$ by (continuous-time) random walk on the 2D box of side length $n$ with wired boundary or on the 2D torus, and show that in both cases with probability approaching 1 as $n$ increases, $\\sqrt{\\tau_{\\mathrm{cov}}}=\\sqrt{2n^2}[\\sqrt{2/\\pi} \\log n + O(\\log\\log n)]$. This improves a result of Dembo, Peres, Rosen, and Zeitouni (2004) and makes progress towards a conjecture of Bramson and Zeitouni (2009).",
  "revisions": [
    {
      "version": "v2",
      "updated": "2012-06-05T21:06:25.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60J10",
      "60G60",
      "60G15"
    ],
    "keywords": [
      "cover time",
      "2d lattices",
      "2d box",
      "side length",
      "2d torus"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 21,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1110.3367D"
    }
  }
}