{
  "id": "1303.4908",
  "version": "v3",
  "published": "2013-03-20T11:27:25.000Z",
  "updated": "2014-09-09T08:11:55.000Z",
  "title": "The Large Connectivity Limit of the Anderson Model on Tree Graphs",
  "authors": [
    "Victor Bapst"
  ],
  "comment": "20 pages, 3 figures (published version)",
  "journal": "J. Math. Phys. 55, 092101 (2014)",
  "doi": "10.1063/1.4894055",
  "categories": [
    "math.PR",
    "cond-mat.dis-nn",
    "cond-mat.stat-mech",
    "math-ph",
    "math.MP"
  ],
  "abstract": "We consider the Anderson localization problem on the infinite regular tree. Within the localized phase, we derive a rigorous lower bound on the free energy function recently introduced by Aizenman and Warzel. Using a finite volume regularization, we also derive an upper bound on this free energy function. This yields upper and lower bounds on the critical disorder such that all states at a given energy become localized. These bounds are particularly useful in the large connectivity limit where they match, confirming the early predictions of Abou-Chacra, Anderson and Thouless.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2013-09-12T20:40:54.000Z",
      "comment": "19 pages, 3 figures (improved results)",
      "journal": null,
      "doi": null
    },
    {
      "version": "v3",
      "updated": "2014-09-09T08:11:55.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "large connectivity limit",
      "anderson model",
      "tree graphs",
      "free energy function",
      "lower bound"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "AIP",
      "journal": "Journal of Mathematical Physics",
      "year": 2014,
      "month": "Sep",
      "volume": 55,
      "number": 9,
      "pages": "092101"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014JMP....55i2101B"
    }
  }
}