{
  "id": "0905.4666",
  "version": "v3",
  "published": "2009-05-28T15:24:38.000Z",
  "updated": "2009-12-11T16:21:08.000Z",
  "title": "Statistical Mechanics of the Chinese Restaurant Process: lack of self-averaging, anomalous finite-size effects and condensation",
  "authors": [
    "Bruno Bassetti",
    "Mina Zarei",
    "Marco Cosentino Lagomarsino",
    "Ginestra Bianconi"
  ],
  "comment": "(5pages, 1 figure)",
  "categories": [
    "cond-mat.dis-nn",
    "cond-mat.stat-mech"
  ],
  "abstract": "The Pitman-Yor, or Chinese Restaurant Process, is a stochastic process that generates distributions following a power-law with exponents lower than two, as found in a numerous physical, biological, technological and social systems. We discuss its rich behavior with the tools and viewpoint of statistical mechanics. We show that this process invariably gives rise to a condensation, i.e. a distribution dominated by a finite number of classes. We also evaluate thoroughly the finite-size effects, finding that the lack of stationary state and self-averaging of the process creates realization-dependent cutoffs and behavior of the distributions with no equivalent in other statistical mechanical models.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2009-12-11T16:21:08.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "89.75.Hc",
      "89.75.Da",
      "89.75.Fb"
    ],
    "keywords": [
      "chinese restaurant process",
      "anomalous finite-size effects",
      "statistical mechanics",
      "condensation",
      "process creates realization-dependent cutoffs"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "doi": "10.1103/PhysRevE.80.066118",
      "journal": "Physical Review E",
      "year": 2009,
      "month": "Dec",
      "volume": 80,
      "number": 6,
      "pages": "066118"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 5,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009PhRvE..80f6118B"
    }
  }
}