{
  "id": "math/0105111",
  "version": "v1",
  "published": "2001-05-13T16:46:16.000Z",
  "updated": "2001-05-13T16:46:16.000Z",
  "title": "Asymptotics of certain coagulation-fragmentation processes and invariant Poisson-Dirichlet measures",
  "authors": [
    "Eddy Mayer-Wolf",
    "Ofer Zeitouni",
    "Martin P. W. Zerner"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "We consider Markov chains on the space of (countable) partitions of the interval $[0,1]$, obtained first by size biased sampling twice (allowing repetitions) and then merging the parts with probability $\\beta_m$ (if the sampled parts are distinct) or splitting the part with probability $\\beta_s$ according to a law $\\sigma$ (if the same part was sampled twice). We characterize invariant probability measures for such chains. In particular, if $\\sigma$ is the uniform measure then the Poisson-Dirichlet law is an invariant probability measure, and it is unique within a suitably defined class of ``analytic'' invariant measures. We also derive transience and recurrence criteria for these chains.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2001-05-13T16:46:16.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60K35",
      "60J27",
      "60G55"
    ],
    "keywords": [
      "invariant poisson-dirichlet measures",
      "coagulation-fragmentation processes",
      "asymptotics",
      "characterize invariant probability measures",
      "uniform measure"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2001math......5111M"
    }
  }
}