{
  "id": "1011.1196",
  "version": "v2",
  "published": "2010-11-04T16:08:13.000Z",
  "updated": "2012-10-04T00:18:04.000Z",
  "title": "Conditional and uniform quenched CLTs for one-dimensional random walks among random conductances",
  "authors": [
    "Christophe Gallesco",
    "Serguei Popov"
  ],
  "comment": "This paper was updated and split in two parts: see http://arxiv.org/abs/1210.0951 and http://arxiv.org/abs/1210.0591",
  "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{conditional} invariance principle for the random walk, under the condition that it remains positive until time $n$. As a corollary of this result, we study the effect of conditioning the random walk to exceed level $n$ before returning to 0 as $n\\to \\infty$. One of the main tools for proving these conditional limit laws is the \\textit{uniform} quenched functional Central Limit Theorem, that states that the convergence is uniform with respect to the starting point, provided that the starting point is chosen in a certain interval around the origin.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2012-10-04T00:18:04.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60J10",
      "60K37"
    ],
    "keywords": [
      "one-dimensional random walk",
      "uniform quenched clts",
      "random conductances",
      "conditional",
      "quenched functional central limit theorem"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1011.1196G"
    }
  }
}