{
  "id": "1001.2337",
  "version": "v3",
  "published": "2010-01-13T23:38:05.000Z",
  "updated": "2013-03-14T14:41:49.000Z",
  "title": "The genealogy of branching Brownian motion with absorption",
  "authors": [
    "Julien Berestycki",
    "Nathanaël Berestycki",
    "Jason Schweinsberg"
  ],
  "comment": "Published in at http://dx.doi.org/10.1214/11-AOP728 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org)",
  "journal": "Annals of Probability 2013, Vol. 41, No. 2, 527-618",
  "doi": "10.1214/11-AOP728",
  "categories": [
    "math.PR",
    "math-ph",
    "math.MP"
  ],
  "abstract": "We consider a system of particles which perform branching Brownian motion with negative drift and are killed upon reaching zero, in the near-critical regime where the total population stays roughly constant with approximately N particles. We show that the characteristic time scale for the evolution of this population is of order $(\\log N)^3$, in the sense that when time is measured in these units, the scaled number of particles converges to a variant of Neveu's continuous-state branching process. Furthermore, the genealogy of the particles is then governed by a coalescent process known as the Bolthausen-Sznitman coalescent. This validates the nonrigorous predictions by Brunet, Derrida, Muller and Munier for a closely related model.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2013-03-14T14:41:49.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "absorption",
      "total population stays roughly constant",
      "neveus continuous-state branching process",
      "perform branching brownian motion",
      "characteristic time scale"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1001.2337B"
    }
  }
}