{
  "id": "math/0603412",
  "version": "v2",
  "published": "2006-03-16T22:24:28.000Z",
  "updated": "2007-01-10T14:01:37.000Z",
  "title": "Weak survival for branching random walks on graphs",
  "authors": [
    "Daniela Bertacchi",
    "Fabio Zucca"
  ],
  "comment": "20 pages; corrected typos and weakened Definition 3.6",
  "journal": "J.Appl.Prob. 45 n.2 (2008), 481-497",
  "categories": [
    "math.PR"
  ],
  "abstract": "We study weak and strong survival for branching random walks on multigraphs. We prove that, for a large class of multigraphs, weak survival is related to a geometrical parameter of the multigraph and that the existence of a pure weak phase is equivalent to nonamenability. Finally we study weak and strong critical behaviors of the branching random walk.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2007-01-10T14:01:37.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60K35"
    ],
    "keywords": [
      "branching random walk",
      "weak survival",
      "study weak",
      "multigraph",
      "pure weak phase"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math......3412B"
    }
  }
}