{
  "id": "1211.7216",
  "version": "v1",
  "published": "2012-11-30T11:30:41.000Z",
  "updated": "2012-11-30T11:30:41.000Z",
  "title": "On the duality between jump processes on ultrametric spaces and random walks on trees",
  "authors": [
    "Wolfgang Woess"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "The purpose of these notes is to clarify the duality between a natural class of jump processes on compact ultrametric spaces - studied in current work of Bendikov, Girgor'yan and Pittet - and nearest neighbour walks on trees. Processes of this type have appeared in recent work of Kigami. Every compact ultrametric space arises as the boundary of a locally finite tree. The duality arises via the Dirichlet forms: one on the tree associated with a random walk and the other on the boundary of the tree, which is given in terms of the Na\\\"im kernel. Here, it is explained that up to a linear time change by a unique constant, there is a one-to-one correspondence between the above processes and Dirichlet regular random walks.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-11-30T11:30:41.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C05",
      "31C05",
      "60G50",
      "60J50"
    ],
    "keywords": [
      "jump processes",
      "dirichlet regular random walks",
      "compact ultrametric space arises",
      "linear time change",
      "nearest neighbour walks"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1211.7216W"
    }
  }
}