{
  "id": "0911.5255",
  "version": "v1",
  "published": "2009-11-27T12:24:34.000Z",
  "updated": "2009-11-27T12:24:34.000Z",
  "title": "A note on the recurrence of edge reinforced random walks",
  "authors": [
    "Laurent Tournier"
  ],
  "comment": "2 pages",
  "categories": [
    "math.PR"
  ],
  "abstract": "We give a short proof of Theorem 2.1 from [MR07], stating that the linearly edge reinforced random walk (ERRW) on a locally finite graph is recurrent if and only if it returns to its starting point almost surely. This result was proved in [MR07] by means of the much stronger property that the law of the ERRW is a mixture of Markov chains. Our proof only uses this latter property on finite graphs, in which case it is a consequence of De Finetti's theorem on exchangeability.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2009-11-27T12:24:34.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "recurrence",
      "linearly edge reinforced random walk",
      "locally finite graph",
      "finettis theorem",
      "short proof"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 2,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0911.5255T"
    }
  }
}