{
  "id": "math/0602074",
  "version": "v1",
  "published": "2006-02-04T20:28:33.000Z",
  "updated": "2006-02-04T20:28:33.000Z",
  "title": "Large deviations estimates for self-intersection local times for simple random walk in $\\Z^3$",
  "authors": [
    "Amine Asselah"
  ],
  "comment": "23 pages",
  "categories": [
    "math.PR"
  ],
  "abstract": "We obtain large deviations estimates for the self-intersection local times for a symmetric random walk in dimension 3. Also, we show that the main contribution to making the self-intersection large, in a time period of length $n$, comes from sites visited less than some power of $\\log(n)$. This is opposite to the situation in dimensions larger or equal to 5. Finally, we present two applications of our estimates: (i) to moderate deviations estimates for the range of a random walk, and (ii) to moderate deviations for random walk in random sceneries.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2006-02-04T20:28:33.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60K35",
      "82C22",
      "60J25"
    ],
    "keywords": [
      "self-intersection local times",
      "large deviations estimates",
      "simple random walk",
      "symmetric random walk",
      "moderate deviations estimates"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 23,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math......2074A"
    }
  }
}