{
  "id": "1107.2543",
  "version": "v5",
  "published": "2011-07-13T13:21:50.000Z",
  "updated": "2015-08-31T08:49:53.000Z",
  "title": "Convergence in law for the branching random walk seen from its tip",
  "authors": [
    "Thomas Madaule"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "Considering a critical branching random walk on the real line. In a recent paper, Aidekon [3] developed a powerful method to obtain the convergence in law of its minimum after a log-factor normalization. By an adaptation of this method, we show that the point process formed by the branching random walk and its minimum converge in law to a Poisson point process colored by a certain point process. This result, confirming a conjecture of Brunet and Derrida [10], can be viewed as a discrete analog of the corresponding results for the branching brownian motion, previously established by Arguin et al. [5] [6] and Aidekon et al. [2].",
  "revisions": [
    {
      "version": "v4",
      "updated": "2013-08-06T07:11:19.000Z",
      "comment": "arXiv admin note: text overlap with arXiv:1101.1810 by other authors",
      "journal": null,
      "doi": null
    },
    {
      "version": "v5",
      "updated": "2015-08-31T08:49:53.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "convergence",
      "minimum converge",
      "log-factor normalization",
      "brownian motion",
      "real line"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1107.2543M"
    }
  }
}