{
  "id": "0810.2467",
  "version": "v1",
  "published": "2008-10-14T15:23:43.000Z",
  "updated": "2008-10-14T15:23:43.000Z",
  "title": "Parabolic Harnack Inequality and Local Limit Theorem for Percolation Clusters",
  "authors": [
    "Martin Barlow",
    "Ben Hambly"
  ],
  "comment": "29 pages",
  "categories": [
    "math.PR",
    "math.AP"
  ],
  "abstract": "We consider the random walk on supercritical percolation clusters in the d-dimensional Euclidean lattice. Previous papers have obtained Gaussian heat kernel bounds, and a.s. invariance principles for this process. We show how this information leads to a parabolic Harnack inequality, a local limit theorem and estimates on the Green's function.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2008-10-14T15:23:43.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60G50",
      "31C25"
    ],
    "keywords": [
      "local limit theorem",
      "parabolic harnack inequality",
      "gaussian heat kernel bounds",
      "d-dimensional euclidean lattice",
      "greens function"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 29,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0810.2467B"
    }
  }
}