{
  "id": "1210.0951",
  "version": "v1",
  "published": "2012-10-03T00:54:20.000Z",
  "updated": "2012-10-03T00:54:20.000Z",
  "title": "Random walks with unbounded jumps among random conductances I: Uniform quenched CLT",
  "authors": [
    "Christophe Gallesco",
    "Serguei Popov"
  ],
  "comment": "arXiv admin note: substantial text overlap with arXiv:1011.1196",
  "journal": "Electronic Journal of Probability, vol. 17, article 85, p. 1-22, 2012",
  "doi": "10.1214/EJP.v17-1826",
  "categories": [
    "math.PR"
  ],
  "abstract": "We study a one-dimensional random walk among random conductances, with unbounded jumps. Assuming the ergodicity of the collection of conductances and a few other technical conditions (uniform ellipticity and polynomial bounds on the tails of the jumps) we prove a quenched \\textit{uniform} invariance principle for the random walk. This means that the rescaled trajectory of length $n$ is (in a certain sense) close enough to the Brownian motion, uniformly with respect to the choice of the starting location in an interval of length $O(\\sqrt{n})$ around the origin.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-10-03T00:54:20.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60J10",
      "60K37"
    ],
    "keywords": [
      "uniform quenched clt",
      "random conductances",
      "unbounded jumps",
      "one-dimensional random walk",
      "uniform ellipticity"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1210.0951G"
    }
  }
}