{
  "id": "1905.10120",
  "version": "v1",
  "published": "2019-05-24T10:04:28.000Z",
  "updated": "2019-05-24T10:04:28.000Z",
  "title": "Convergence towards the end space for random walks on Schreier graphs",
  "authors": [
    "Bogdan Stankov"
  ],
  "comment": "8 pages, 2 figures",
  "categories": [
    "math.GR",
    "math.PR"
  ],
  "abstract": "We consider a transitive action of a finitely generated group $G$ and the Schreier graph $\\Gamma$ it defines. For a probability measure $\\mu$ on $G$ with a finite first moment we show that if the induced random walk is transient, it converges towards the space of ends of $\\Gamma$. As a corollary we obtain that for a probability measure on Thompson's group $F$ with a finite first moment, the support of which generates $F$ as a semigroup, the induced random walk on the dyadic numbers has a non-trivial Poisson boundary. Some assumption on the moment of the measure is necessary as follows from an example by Juschenko and Zheng.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-05-24T10:04:28.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C81",
      "60B15",
      "60J50",
      "05C25",
      "20F65",
      "60J10"
    ],
    "keywords": [
      "schreier graph",
      "end space",
      "finite first moment",
      "induced random walk",
      "convergence"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 8,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}