{
  "id": "0807.4278",
  "version": "v3",
  "published": "2008-07-27T07:27:41.000Z",
  "updated": "2012-07-20T13:06:08.000Z",
  "title": "The $Λ$-coalescent speed of coming down from infinity",
  "authors": [
    "Julien Berestycki",
    "Nathanaël Berestycki",
    "Vlada Limic"
  ],
  "comment": "Published in at http://dx.doi.org/10.1214/09-AOP475 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org)",
  "journal": "Annals of Probability 2010, Vol. 38, No. 1, 207-233",
  "doi": "10.1214/09-AOP475",
  "categories": [
    "math.PR"
  ],
  "abstract": "Consider a $\\Lambda$-coalescent that comes down from infinity (meaning that it starts from a configuration containing infinitely many blocks at time 0, yet it has a finite number $N_t$ of blocks at any positive time $t>0$). We exhibit a deterministic function $v:(0,\\infty)\\to(0,\\infty)$ such that $N_t/v(t)\\to1$, almost surely, and in $L^p$ for any $p\\geq1$, as $t\\to0$. Our approach relies on a novel martingale technique.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2012-07-20T13:06:08.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "coalescent",
      "novel martingale technique",
      "deterministic function",
      "approach relies",
      "finite number"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0807.4278B"
    }
  }
}