{
  "id": "math/0503576",
  "version": "v5",
  "published": "2005-03-25T02:00:39.000Z",
  "updated": "2006-02-20T22:58:46.000Z",
  "title": "Quenched invariance principle for simple random walk on percolation clusters",
  "authors": [
    "Noam Berger",
    "Marek Biskup"
  ],
  "comment": "38 pages (PTRF format) 4 figures. Version to appear in PTRF",
  "journal": "Probab. Theory Rel. Fields 137 (2007), no. 1-2, 83-120",
  "doi": "10.1007/s00440-006-0498-z",
  "categories": [
    "math.PR",
    "math-ph",
    "math.MP"
  ],
  "abstract": "We consider the simple random walk on the (unique) infinite cluster of super-critical bond percolation in $\\Z^d$ with $d\\ge2$. We prove that, for almost every percolation configuration, the path distribution of the walk converges weakly to that of non-degenerate, isotropic Brownian motion. Our analysis is based on the consideration of a harmonic deformation of the infinite cluster on which the random walk becomes a square-integrable martingale. The size of the deformation, expressed by the so called corrector, is estimated by means of ergodicity arguments.",
  "revisions": [
    {
      "version": "v5",
      "updated": "2006-02-20T22:58:46.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60K37",
      "60F17",
      "82C41"
    ],
    "keywords": [
      "simple random walk",
      "quenched invariance principle",
      "percolation clusters",
      "infinite cluster",
      "isotropic brownian motion"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 38,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2005math......3576B"
    }
  }
}