{
  "id": "math/0703741",
  "version": "v3",
  "published": "2007-03-25T21:16:02.000Z",
  "updated": "2007-09-21T16:46:15.000Z",
  "title": "A dynamical characterization of Poisson-Dirichlet distributions",
  "authors": [
    "Louis-Pierre Arguin"
  ],
  "comment": "8 pages; final version accepted for publication",
  "journal": "Electr. Comm. Prob. 12 (2007) 283-290",
  "categories": [
    "math.PR"
  ],
  "abstract": "We show that a slight modification of a theorem of Ruzmaikina and Aizenman on competing particle systems on the real line leads to a characterization of Poisson-Dirichlet distributions $PD(a,0)$. Precisely, let $s$ be a proper random mass-partition i.e. a random sequence $(s_i, i\\in\\N)$ such that $s_1\\geq s_2\\geq ...$ and $\\sum_i s_i=1$ a.s. Consider ${W_i}_{i\\in\\N}$, an iid sequence of positive random variables with a density and such that $E[W^\\lambda]$ is finite for all $\\lambda\\in\\R$. It is shown that if the law of $s$ is invariant under a random multiplicative shift $s_i W_i$ of the atoms followed by a renormalization, then it must be a mixture of Poisson-Dirichlet distribution $PD(a,0)$, $a\\in (0,1)$.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2007-09-21T16:46:15.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60G55",
      "60K35"
    ],
    "keywords": [
      "poisson-dirichlet distribution",
      "dynamical characterization",
      "proper random mass-partition",
      "positive random variables",
      "iid sequence"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 8,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007math......3741A"
    }
  }
}