{
  "id": "1005.4659",
  "version": "v1",
  "published": "2010-05-25T19:01:14.000Z",
  "updated": "2010-05-25T19:01:14.000Z",
  "title": "On the local time of random walks associated with Gegenbauer polynomials",
  "authors": [
    "Nadine Guillotin-Plantard"
  ],
  "comment": "12 pages",
  "categories": [
    "math.PR"
  ],
  "abstract": "The local time of random walks associated with Gegenbauer polynomials $P_n^{(\\alpha)}(x),\\ x\\in [-1,1]$ is studied in the recurrent case: $\\alpha\\in\\ [-\\frac{1}{2},0]$. When $\\alpha$ is nonzero, the limit distribution is given in terms of a Mittag-Leffler distribution. The proof is based on a local limit theorem for the random walk associated with Gegenbauer polynomials. As a by-product, we derive the limit distribution of the local time of some particular birth and death Markov chains on $\\bbN$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2010-05-25T19:01:14.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "random walks",
      "gegenbauer polynomials",
      "local time",
      "limit distribution",
      "local limit theorem"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1005.4659G"
    }
  }
}