{
  "id": "1301.1506",
  "version": "v2",
  "published": "2013-01-08T12:13:40.000Z",
  "updated": "2014-01-23T11:45:24.000Z",
  "title": "The Boundary of a Square Tiling of a Graph coincides with the Poisson Boundary",
  "authors": [
    "Agelos Georgakopoulos"
  ],
  "comment": "Section 8 added in version 2",
  "categories": [
    "math.PR",
    "math.CO"
  ],
  "abstract": "Answering a question of Benjamini & Schramm [8], we show that the Poisson boundary of any planar, uniquely absorbing (e.g. one-ended and transient) graph with bounded degrees can be realised geometrically as a circle, namely as the boundary of a tiling of a cylinder by squares. This implies a conjecture of Northshield [34] of similar flavour. For our proof we introduce a general criterion for identifying the Poisson boundary of a stochastic process that might have further applications.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2014-01-23T11:45:24.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60J50",
      "60J10",
      "05C10"
    ],
    "keywords": [
      "poisson boundary",
      "graph coincides",
      "square tiling",
      "similar flavour",
      "general criterion"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1301.1506G"
    }
  }
}