{
  "id": "1508.01845",
  "version": "v1",
  "published": "2015-08-08T01:16:15.000Z",
  "updated": "2015-08-08T01:16:15.000Z",
  "title": "Poisson Boundaries of Lamplighter Groups: Proof of the Kaimanovich-Vershik Conjecture",
  "authors": [
    "Russell Lyons",
    "Yuval Peres"
  ],
  "comment": "20 pages",
  "categories": [
    "math.PR"
  ],
  "abstract": "We answer positively a question of Kaimanovich and Vershik from 1979, showing that the final configuration of lamps for simple random walk on the lamplighter group over ${\\Bbb Z}^d$ ($d \\ge 3$) is the Poisson boundary. For $d \\ge 5$, this had been shown earlier by Erschler (2011). We extend this to walks of more general types on more general groups.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-08-08T01:16:15.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20F69",
      "60B15",
      "60J50",
      "43A05",
      "20F65"
    ],
    "keywords": [
      "lamplighter group",
      "poisson boundary",
      "kaimanovich-vershik conjecture",
      "simple random walk",
      "final configuration"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150801845L"
    }
  }
}