{
  "id": "1609.06706",
  "version": "v1",
  "published": "2016-09-21T19:58:20.000Z",
  "updated": "2016-09-21T19:58:20.000Z",
  "title": "Diffusions on a space of interval partitions with Poisson-Dirichlet stationary distributions",
  "authors": [
    "Noah Forman",
    "Soumik Pal",
    "Douglas Rizzolo",
    "Matthias Winkel"
  ],
  "comment": "78 pages, 8 figures",
  "categories": [
    "math.PR"
  ],
  "abstract": "We construct a pair of related diffusions on a space of interval partitions of the unit interval $[0,1]$ that are stationary with the Poisson-Dirichlet laws with parameters (1/2,0) and (1/2,1/2) respectively. These are two particular cases of a general construction of such processes obtained by decorating the jumps of a spectrally positive L\\'evy process with independent squared Bessel excursions. The processes of ranked interval lengths of our partitions are members of a two parameter family of diffusions introduced by Ethier and Kurtz (1981) and Petrov (2009). The latter diffusions are continuum limits of up-down Markov chains on Chinese restaurant processes. Our construction is also a step towards describing a diffusion on the space of real trees whose existence has been conjectured by Aldous.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-09-21T19:58:20.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60J25",
      "60J60",
      "60J80",
      "60G18",
      "60G52",
      "60G55"
    ],
    "keywords": [
      "poisson-dirichlet stationary distributions",
      "interval partitions",
      "chinese restaurant processes",
      "up-down markov chains",
      "independent squared bessel excursions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 78,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}