{
  "id": "1001.2459",
  "version": "v1",
  "published": "2010-01-14T14:03:53.000Z",
  "updated": "2010-01-14T14:03:53.000Z",
  "title": "Scaling limit of the random walk among random traps on Z^d",
  "authors": [
    "Jean-Christophe Mourrat"
  ],
  "comment": "40 pages",
  "categories": [
    "math.PR"
  ],
  "abstract": "Attributing a positive value \\tau_x to each x in Z^d, we investigate a nearest-neighbour random walk which is reversible for the measure with weights (\\tau_x), often known as \"Bouchaud's trap model\". We assume that these weights are independent, identically distributed and non-integrable random variables (with polynomial tail), and that d > 4. We obtain the quenched subdiffusive scaling limit of the model, the limit being the fractional kinetics process. We begin our proof by expressing the random walk as a time change of a random walk among random conductances. We then focus on proving that the time change converges, under the annealed measure, to a stable subordinator. This is achieved using previous results concerning the mixing properties of the environment viewed by the time-changed random walk.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2010-01-14T14:03:53.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60K37",
      "60G52",
      "60F17",
      "82D30"
    ],
    "keywords": [
      "scaling limit",
      "random traps",
      "bouchauds trap model",
      "nearest-neighbour random walk",
      "fractional kinetics process"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 40,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011AnIHP..47..813M"
    }
  }
}