{
  "id": "1109.6725",
  "version": "v2",
  "published": "2011-09-30T06:43:53.000Z",
  "updated": "2012-03-14T06:32:48.000Z",
  "title": "Cayley Trees and Bethe Lattices, a concise analysis for mathematicians and physicists",
  "authors": [
    "Massimo Ostilli"
  ],
  "comment": "10 pages, 2 figures",
  "journal": "Physica A, 391, 3417 (2012)",
  "doi": "10.1016/j.physa.2012.01.038",
  "categories": [
    "cond-mat.stat-mech",
    "cond-mat.dis-nn",
    "math-ph",
    "math.MP"
  ],
  "abstract": "We review critically the concepts and the applications of Cayley Trees and Bethe Lattices in statistical mechanics in a tentative effort to remove widespread misuse of these simple, but yet important - and different - ideal graphs. We illustrate, in particular, two rigorous techniques to deal with Bethe Lattices, based respectively on self-similarity and on the Kolmogorov consistency theorem, linking the latter with the Cavity and Belief Propagation methods, more known to the physics community.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2012-03-14T06:32:48.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "82B23"
    ],
    "keywords": [
      "bethe lattices",
      "cayley trees",
      "concise analysis",
      "mathematicians",
      "physicists"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "journal": "Physica A Statistical Mechanics and its Applications",
      "year": 2012,
      "month": "Jun",
      "volume": 391,
      "number": 12,
      "pages": 3417
    },
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012PhyA..391.3417O"
    }
  }
}