{
  "id": "0904.1526",
  "version": "v1",
  "published": "2009-04-09T13:33:56.000Z",
  "updated": "2009-04-09T13:33:56.000Z",
  "title": "Kingman's coalescent and Brownian motion",
  "authors": [
    "J. Berestycki",
    "N. Berestycki"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "We describe a simple construction of Kingman's coalescent in terms of a Brownian excursion. This construction is closely related to, and sheds some new light on, earlier work by Aldous and Warren. Our approach also yields some new results: for instance, we obtain the full multifractal spectrum of Kingman's coalescent. This complements earlier work on Beta-coalescents by the authors and Schweinsberg. Surprisingly, the thick part of the spectrum is not obtained by taking the limit as $\\alpha \\to 2$ in the result for Beta-coalescents mentioned above. Other analogies and differences between the case of Beta-coalescents and Kingman's coalescent are discussed.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2009-04-09T13:33:56.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60J25",
      "60G15"
    ],
    "keywords": [
      "kingmans coalescent",
      "brownian motion",
      "full multifractal spectrum",
      "complements earlier work",
      "beta-coalescents"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}