{
  "id": "1302.1463",
  "version": "v1",
  "published": "2013-02-06T18:20:44.000Z",
  "updated": "2013-02-06T18:20:44.000Z",
  "title": "Total internal and external lengths of the Bolthausen-Sznitman coalescent",
  "authors": [
    "Götz Kersting",
    "Juan Carlos Pardo",
    "Arno Siri-Jégousse"
  ],
  "categories": [
    "math.PR",
    "q-bio.PE"
  ],
  "abstract": "In this paper, we study a weak law of large numbers for the total internal length of the Bolthausen-Szmitman coalescent. As a consequence, we obtain the weak limit law of the centered and rescaled total external length. The latter extends results obtained by Dhersin & M\\\"ohle \\cite{DM12}. An application to population genetics dealing with the total number of mutations in the genealogical tree is also given.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-02-06T18:20:44.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "bolthausen-sznitman coalescent",
      "total internal length",
      "weak limit law",
      "rescaled total external length",
      "weak law"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1302.1463K"
    }
  }
}