{
  "id": "1206.5182",
  "version": "v2",
  "published": "2012-06-22T15:44:53.000Z",
  "updated": "2013-03-06T14:04:58.000Z",
  "title": "A local limit theorem for random walks in balanced environments",
  "authors": [
    "Mikko Stenlund"
  ],
  "comment": "12 pages, 1 figure. A discrete time version of the main result added in this version. To appear in Electronic Communications in Probability",
  "categories": [
    "math.PR",
    "math-ph",
    "math.AP",
    "math.MP"
  ],
  "abstract": "Central limit theorems for random walks in quenched random environments have attracted plenty of attention in the past years. More recently still, finer local limit theorems -- yielding a Gaussian density multiplied by a highly oscillatory modulating factor -- for such models have been obtained. In the one-dimensional nearest-neighbor case with i.i.d. transition probabilities, local limits of uniformly elliptic ballistic walks are now well understood. We complete the picture by proving a similar result for the only recurrent case, namely the balanced one, in which such a walk is diffusive. The method of proof is, out of necessity, entirely different from the ballistic case.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2013-03-06T14:04:58.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60K37",
      "60F15",
      "82C41",
      "82D30",
      "35K15"
    ],
    "keywords": [
      "random walks",
      "balanced environments",
      "finer local limit theorems",
      "central limit theorems",
      "uniformly elliptic ballistic walks"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1206.5182S"
    }
  }
}