{
  "id": "1306.5266",
  "version": "v2",
  "published": "2013-06-21T22:17:15.000Z",
  "updated": "2013-11-07T15:00:37.000Z",
  "title": "On large deviations for the cover time of two-dimensional torus",
  "authors": [
    "Francis Comets",
    "Christophe Gallesco",
    "Serguei Popov",
    "Marina Vachkovskaia"
  ],
  "comment": "25 pages, 5 figures",
  "journal": "Electronic Journal of Probability, Vol. 18, Article 96, pp.1-18 (2013)",
  "doi": "10.1214/EJP.v18-2856",
  "categories": [
    "math.PR"
  ],
  "abstract": "Let $\\mathcal{T}_n$ be the cover time of two-dimensional discrete torus $\\mathbb{Z}^2_n=\\mathbb{Z}^2/n\\mathbb{Z}^2$. We prove that $\\mathbb{P}[\\mathcal{T}_n\\leq \\frac{4}{\\pi}\\gamma n^2\\ln^2 n]=\\exp(-n^{2(1-\\sqrt{\\gamma})+o(1)})$ for $\\gamma\\in (0,1)$. One of the main methods used in the proofs is the decoupling of the walker's trace into independent excursions by means of soft local times.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2013-11-07T15:00:37.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60G50",
      "82C41",
      "60G55"
    ],
    "keywords": [
      "cover time",
      "large deviations",
      "two-dimensional torus",
      "two-dimensional discrete torus",
      "soft local times"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 25,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1306.5266C"
    }
  }
}