{
  "id": "1712.07553",
  "version": "v1",
  "published": "2017-12-20T16:14:47.000Z",
  "updated": "2017-12-20T16:14:47.000Z",
  "title": "On the time to absorption in $Λ$-coalescents",
  "authors": [
    "Götz Kersting",
    "Anton Wakolbinger"
  ],
  "comment": "15 pages",
  "categories": [
    "math.PR"
  ],
  "abstract": "We present a law of large numbers and a central limit theorem for the time to absorption of $\\Lambda$-coalescents, started from $n$ blocks, as $n \\to \\infty$. The proofs rely on an approximation of the logarithm of the block-counting process of $\\Lambda$-coalescents with a dust component by means of a drifted subordinator.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-12-20T16:14:47.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60J75",
      "60J27",
      "60F05"
    ],
    "keywords": [
      "coalescents",
      "absorption",
      "central limit theorem",
      "large numbers",
      "dust component"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}