{
  "id": "1004.5011",
  "version": "v2",
  "published": "2010-04-28T12:26:27.000Z",
  "updated": "2011-01-17T15:08:45.000Z",
  "title": "The external lengths in Kingman's coalescent",
  "authors": [
    "Svante Janson",
    "Götz Kersting"
  ],
  "comment": "Author added, new approach to the urn model, new proof of the main reversibility result",
  "categories": [
    "math.PR"
  ],
  "abstract": "In this paper we prove asymptotic normality of the total length of external branches in Kingman's coalescent. The proof uses an embedded Markov chain, which can be descriped as follows: Take an urn with n black balls. Empty it in n steps according to the rule: In each step remove a randomly chosen pair of balls and replace it by one red ball. Finally remove the last remaining ball. Then the numbers U_k, 0 \\leq k \\leq n, of red balls after k steps exhibits an unexpected property: (U_0,...,U_n) and (U_n,..., U_0) are equal in distribution.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2011-01-17T15:08:45.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60K35",
      "60F05",
      "60J10"
    ],
    "keywords": [
      "kingmans coalescent",
      "external lengths",
      "red ball",
      "step remove",
      "asymptotic normality"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1004.5011J"
    }
  }
}