{
  "id": "math/0612856",
  "version": "v1",
  "published": "2006-12-29T17:16:31.000Z",
  "updated": "2006-12-29T17:16:31.000Z",
  "title": "Condensation for a fixed number of independent random variables",
  "authors": [
    "Pablo A. Ferrari",
    "Claudio Landim",
    "Valentin V. Sisko"
  ],
  "comment": "6 pages",
  "journal": "Journal of Statistical Physics 2007, v. 128, p. 1153-1158",
  "doi": "10.1007/s10955-007-9356-3",
  "categories": [
    "math.PR",
    "math-ph",
    "math.MP"
  ],
  "abstract": "A family of m independent identically distributed random variables indexed by a chemical potential \\phi\\in[0,\\gamma] represents piles of particles. As \\phi increases to \\gamma, the mean number of particles per site converges to a maximal density \\rho_c<\\infty. The distribution of particles conditioned on the total number of particles equal to n does not depend on \\phi (canonical ensemble). For fixed m, as n goes to infinity the canonical ensemble measure behave as follows: removing the site with the maximal number of particles, the distribution of particles in the remaining sites converges to the grand canonical measure with density \\rho_c; the remaining particles concentrate (condensate) on a single site.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2006-12-29T17:16:31.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60K35",
      "82C22"
    ],
    "keywords": [
      "independent random variables",
      "fixed number",
      "condensation",
      "independent identically distributed random variables"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 6,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}