{
  "id": "0704.2337",
  "version": "v1",
  "published": "2007-04-18T12:40:56.000Z",
  "updated": "2007-04-18T12:40:56.000Z",
  "title": "Existence of graphs with sub exponential transitions probability decay and applications",
  "authors": [
    "Clement Rau"
  ],
  "comment": "46 pages",
  "categories": [
    "math.PR"
  ],
  "abstract": "In this paper, we present a complete proof of the construction of graphs with bounded valency such that the simple random walk has a return probability at time $n$ at the origin of order $exp(-n^{\\alpha}),$ for fixed $\\alpha \\in [0,1[$ and with Folner function $exp(n^{\\frac{2\\alpha}{1-\\alpha}})$. We begin by giving a more detailled proof of this result contained in (see \\cite{ershdur}). In the second part, we give an application of the existence of such graphs. We obtain bounds of the correct order for some functional of the local time of a simple random walk on an infinite cluster on the percolation model.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2007-04-18T12:40:56.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60J10",
      "60K35"
    ],
    "keywords": [
      "sub exponential transitions probability decay",
      "simple random walk",
      "application",
      "percolation model",
      "complete proof"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 46,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007arXiv0704.2337R"
    }
  }
}