{
  "id": "1201.1701",
  "version": "v1",
  "published": "2012-01-09T07:31:39.000Z",
  "updated": "2012-01-09T07:31:39.000Z",
  "title": "An ergodic theorem for the frontier of branching Brownian motion",
  "authors": [
    "Louis-Pierre Arguin",
    "Anton Bovier",
    "Nicola Kistler"
  ],
  "comment": "4 figures",
  "categories": [
    "math.PR"
  ],
  "abstract": "We prove a conjecture of Lalley and Sellke [Ann. Probab. 15 (1987)] asserting that the empirical (time-averaged) distribution function of the maximum of branching Brownian motion converges almost surely to a double exponential, or Gumbel, distribution with a random shift. The method of proof is based on the decorrelation of the maximal displacements for appropriate time scales. A crucial input is the localization of the paths of particles close to the maximum that was previously established by the authors [Comm. Pure Appl. Math. 64 (2011)].",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-01-09T07:31:39.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60J80",
      "60G70",
      "82B44"
    ],
    "keywords": [
      "ergodic theorem",
      "appropriate time scales",
      "branching brownian motion converges",
      "random shift",
      "distribution function"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1201.1701A"
    }
  }
}