{
  "id": "0908.3847",
  "version": "v1",
  "published": "2009-08-26T15:03:46.000Z",
  "updated": "2009-08-26T15:03:46.000Z",
  "title": "Appearance of vertices of infinite order in a model of random trees",
  "authors": [
    "Thordur Jonsson",
    "Sigurdur O. Stefansson"
  ],
  "comment": "22 pages, 5 figures",
  "categories": [
    "cond-mat.stat-mech",
    "math-ph",
    "math.MP"
  ],
  "abstract": "We study an equilibrium statistical mechanical model of tree graphs which are made up of a linear subgraph (the spine) to which leaves are attached. We prove that the model has two phases, a generic phase where the spine becomes infinitely long in the thermodynamic limit and all vertices have finite order and a condensed phase where the spine is finite with probability one and a single vertex of infinite order appears in the thermodynamic limit. We calculate the spectral dimension of the graphs in both phases and prove the existence of a Gibbs measure. We discuss generalizations of this model and the relationship with models of nongeneric random trees.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2009-08-26T15:03:46.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "thermodynamic limit",
      "appearance",
      "nongeneric random trees",
      "infinite order appears",
      "tree graphs"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "doi": "10.1088/1751-8113/42/48/485006",
      "journal": "Journal of Physics A Mathematical General",
      "year": 2009,
      "month": "Dec",
      "volume": 42,
      "number": 48,
      "pages": 485006
    },
    "note": {
      "typesetting": "TeX",
      "pages": 22,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009JPhA...42V5006J"
    }
  }
}