{
  "id": "1212.6070",
  "version": "v1",
  "published": "2012-12-25T17:42:12.000Z",
  "updated": "2012-12-25T17:42:12.000Z",
  "title": "The total external branch length of Beta-coalescents",
  "authors": [
    "Götz Kersting",
    "Iulia Stanciu",
    "Anton Wakolbinger"
  ],
  "comment": "17 pages, 2 figures",
  "categories": [
    "math.PR"
  ],
  "abstract": "For $1<\\alpha <2$ we derive the asymptotic distribution of the total length of {\\em external} branches of a Beta$(2-\\alpha, \\alpha)$-coalescent as the number $n$ of leaves becomes large. It turns out the fluctuations of the external branch length follow those of $\\tau_n^{2-\\alpha}$ over the entire parameter regime, where $\\tau_n$ denotes the random number of coalescences that bring the $n$ lineages down to one. This is in contrast to the fluctuation behavior of the total branch length, which exhibits a transition at $\\alpha_0 = (1+\\sqrt 5)/2$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-12-25T17:42:12.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60K35",
      "60F05",
      "60J10"
    ],
    "keywords": [
      "total external branch length",
      "beta-coalescents",
      "total branch length",
      "entire parameter regime",
      "asymptotic distribution"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1212.6070K"
    }
  }
}