{
  "id": "0805.0407",
  "version": "v2",
  "published": "2008-05-04T11:41:20.000Z",
  "updated": "2008-08-18T14:20:45.000Z",
  "title": "Freezing and extreme value statistics in a Random Energy Model with logarithmically correlated potential",
  "authors": [
    "Yan V Fyodorov",
    "Jean-Philippe Bouchaud"
  ],
  "comment": "Published version with a few references added, misprints corrected and a few places more clearly written",
  "journal": "J. Phys.A: Math.Theor 41 (2008) 372001 (12pp)",
  "doi": "10.1088/1751-8113/41/37/372001",
  "categories": [
    "cond-mat.dis-nn",
    "cond-mat.stat-mech",
    "math-ph",
    "math.MP"
  ],
  "abstract": "We investigate some implications of the freezing scenario proposed by Carpentier and Le Doussal (CLD) for a random energy model (REM) with logarithmically correlated random potential. We introduce a particular (circular) variant of the model, and show that the integer moments of the partition function in the high-temperature phase are given by the well-known Dyson Coulomb gas integrals. The CLD freezing scenario allows one to use those moments for extracting the distribution of the free energy in both high- and low-temperature phases. In particular, it yields the full distribution of the minimal value in the potential sequence. This provides an explicit new class of extreme-value statistics for strongly correlated variables, manifestly different from the standard Gumbel class. -",
  "revisions": [
    {
      "version": "v2",
      "updated": "2008-08-18T14:20:45.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "random energy model",
      "extreme value statistics",
      "logarithmically correlated potential",
      "well-known dyson coulomb gas integrals"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "journal": "Journal of Physics A Mathematical General",
      "year": 2008,
      "month": "Sep",
      "volume": 41,
      "number": 37,
      "pages": 372001
    },
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008JPhA...41K2001F"
    }
  }
}