{
  "id": "math/0603363",
  "version": "v1",
  "published": "2006-03-15T09:01:53.000Z",
  "updated": "2006-03-15T09:01:53.000Z",
  "title": "A subdiffusive behaviour of recurrent random walk in random environment on a regular tree",
  "authors": [
    "Yueyun Hu",
    "Zhan Shi"
  ],
  "comment": "29 pages with 1 figure. Its preliminary version was put in the following web site: http://www.math.univ-paris13.fr/prepub/pp2005/pp2005-28.html",
  "categories": [
    "math.PR"
  ],
  "abstract": "We are interested in the random walk in random environment on an infinite tree. Lyons and Pemantle [11] give a precise recurrence/transience criterion. Our paper focuses on the almost sure asymptotic behaviours of a recurrent random walk $(X\\_n)$ in random environment on a regular tree, which is closely related to Mandelbrot [13]'s multiplicative cascade. We prove, under some general assumptions upon the distribution of the environment, the existence of a new exponent $\\nu\\in (0, {1\\over 2}]$ such that $\\max\\_{0\\le i \\le n} |X\\_i|$ behaves asymptotically like $n^{\\nu}$. The value of $\\nu$ is explicitly formulated in terms of the distribution of the environment.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2006-03-15T09:01:53.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60K37",
      "60G50"
    ],
    "keywords": [
      "recurrent random walk",
      "random environment",
      "regular tree",
      "subdiffusive behaviour",
      "sure asymptotic behaviours"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 29,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math......3363H"
    }
  }
}