{
  "id": "0905.1297",
  "version": "v1",
  "published": "2009-05-08T17:17:44.000Z",
  "updated": "2009-05-08T17:17:44.000Z",
  "title": "Central Limit Theorems for Gromov Hyperbolic Groups",
  "authors": [
    "Michael Bjorklund"
  ],
  "comment": "Accepted in Journal of Theoretical Probability",
  "categories": [
    "math.PR",
    "math.MG"
  ],
  "abstract": "In this paper we study asymptotic properties of symmetric and non-degenerate random walks on transient hyperbolic groups. We prove a central limit theorem and a law of iterated logarithm for the drift of a random walk, extending previous results by S. Sawyer and T. Steger and F. Ledrappier for certain CAT minus one groups. The proofs use a result by A. Ancona on the identification of the Martin boundary of a hyperbolic group with its Gromov boundary. We also give a new interpretation, in terms of Hilbert metrics, of the Green metric, first introduced by S. Brofferio and S. Blachere.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2009-05-08T17:17:44.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "central limit theorem",
      "gromov hyperbolic groups",
      "non-degenerate random walks",
      "transient hyperbolic groups",
      "study asymptotic properties"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0905.1297B"
    }
  }
}