{
  "id": "0902.2285",
  "version": "v1",
  "published": "2009-02-13T10:04:16.000Z",
  "updated": "2009-02-13T10:04:16.000Z",
  "title": "A note on the Poisson boundary of lamplighter random walks",
  "authors": [
    "Ecaterina Sava"
  ],
  "comment": "18 pages, no figures",
  "journal": "Monatshefte fuer Mathematik 159 (2010), 329-344",
  "doi": "10.1007/s00605-009-0103-5",
  "categories": [
    "math.PR"
  ],
  "abstract": "The main goal of this paper is to determine the Poisson boundary of lamplighter random walks over a general class of discrete groups $\\Gamma$ endowed with a rich boundary. The starting point is the Strip Criterion of identification of the Poisson boundary for random walks on discrete groups due to Kaimanovich. A geometrical method for constructing the strip as a subset of the lamplighter group starting with a smaller strip in the base group $\\Gamma$ is developed. Then, this method is applied to several classes of base groups $\\Gamma$: groups with infinitely many ends, hyperbolic groups in the sense of Gromov, and Euclidean lattices. We show that under suitable hypothesis the Poisson boundary for a class of random walks on lamplighter groups is the space of infinite limit configurations.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2009-02-13T10:04:16.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60J50",
      "60B15",
      "05C05",
      "20E08"
    ],
    "keywords": [
      "lamplighter random walks",
      "poisson boundary",
      "discrete groups",
      "lamplighter group",
      "base group"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 18,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0902.2285S"
    }
  }
}