{
  "id": "2101.09307",
  "version": "v1",
  "published": "2021-01-22T19:49:02.000Z",
  "updated": "2021-01-22T19:49:02.000Z",
  "title": "Ranked masses in two-parameter Fleming-Viot diffusions",
  "authors": [
    "Noah Forman",
    "Soumik Pal",
    "Douglas Rizzolo",
    "Matthias Winkel"
  ],
  "comment": "20 pages",
  "categories": [
    "math.PR"
  ],
  "abstract": "In previous work, we constructed Fleming--Viot-type measure-valued diffusions (and diffusions on a space of interval partitions of the unit interval $[0,1]$) that are stationary with the Poisson--Dirichlet laws with parameters $\\alpha\\in(0,1)$ and $\\theta\\geq 0$. In this paper, we complete the proof that these processes resolve a conjecture by Feng and Sun (2010) by showing that the processes of ranked atom sizes (or of ranked interval lengths) of these diffusions are members of a two-parameter family of diffusions introduced by Petrov (2009), extending a model by Ethier and Kurtz (1981) in the case $\\alpha=0$. The latter diffusions are continuum limits of up-down Chinese restaurant processes.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-01-22T19:49:02.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60J25",
      "60J60",
      "60G55",
      "60J35",
      "60J80"
    ],
    "keywords": [
      "two-parameter fleming-viot diffusions",
      "ranked masses",
      "up-down chinese restaurant processes",
      "constructed fleming-viot-type measure-valued diffusions",
      "interval partitions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}