{
  "id": "1004.4845",
  "version": "v1",
  "published": "2010-04-27T16:10:18.000Z",
  "updated": "2010-04-27T16:10:18.000Z",
  "title": "An asymptotic variance of the self-intersections of random walks",
  "authors": [
    "George Deligiannidis",
    "Sergey Utev"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "We present a Darboux-Wiener type lemma and apply it to obtain an exact asymptotic for the variance of the self-intersection of one and two-dimensional random walks. As a corollary, we obtain a central limit theorem for random walk in random scenery conjectured by Kesten and Spitzer in 1979.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2010-04-27T16:10:18.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "asymptotic variance",
      "self-intersection",
      "central limit theorem",
      "two-dimensional random walks",
      "darboux-wiener type lemma"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1004.4845D"
    }
  }
}