{
  "id": "1912.10410",
  "version": "v1",
  "published": "2019-12-22T10:10:15.000Z",
  "updated": "2019-12-22T10:10:15.000Z",
  "title": "Martin boundary of killed random walks on isoradial graphs",
  "authors": [
    "Cédric Boutillier",
    "Kilian Raschel"
  ],
  "comment": "With an appendix by Alin Bostan. 25 pages, 7 figures",
  "categories": [
    "math.PR",
    "math-ph",
    "math.MP"
  ],
  "abstract": "We consider killed planar random walks on isoradial graphs. Contrary to the lattice case, isoradial graphs are not translation invariant, do not admit any group structure and are spatially non-homogeneous. Despite these crucial differences, we compute the asymptotics of the Martin kernel, deduce the Martin boundary and show that it is minimal. Similar results on the grid $\\mathbb Z^d$ are derived in a celebrated work of Ney and Spitzer.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-12-22T10:10:15.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "isoradial graphs",
      "killed random walks",
      "martin boundary",
      "killed planar random walks",
      "translation invariant"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 25,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}