{
  "id": "1308.2282",
  "version": "v2",
  "published": "2013-08-10T06:54:33.000Z",
  "updated": "2013-11-01T11:13:13.000Z",
  "title": "Large deviations for simple random walk on percolations with long-range correlations",
  "authors": [
    "Kazuki Okamura"
  ],
  "comment": "12 pages, New theorem added",
  "categories": [
    "math.PR"
  ],
  "abstract": "We show quenched large deviations for the simple random walk on a certain class of percolations with long-range correlations. This class contains the supercritical Bernoulli percolations, the model considered by Drewitz, R'ath and Sapozhnikov and the random-cluster model up to the slab critical point. Our result is an extension of Kubota's result for the supercritical Bernoulli percolations. We also state a shape theorem for the chemical distance, which is an extension of Garet and Marchand's result for the supercritical Bernoulli percolations.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2013-11-01T11:13:13.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60K37",
      "60K35"
    ],
    "keywords": [
      "simple random walk",
      "long-range correlations",
      "supercritical bernoulli percolations",
      "marchands result",
      "shape theorem"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1308.2282O"
    }
  }
}