{
  "id": "0712.2582",
  "version": "v3",
  "published": "2007-12-16T16:48:34.000Z",
  "updated": "2009-07-24T15:06:28.000Z",
  "title": "Minima in branching random walks",
  "authors": [
    "Louigi Addario-Berry",
    "Bruce Reed"
  ],
  "comment": "Published in at http://dx.doi.org/10.1214/08-AOP428 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org)",
  "journal": "Annals of Probability 2009, Vol. 37, No. 3, 1044-1079",
  "doi": "10.1214/08-AOP428",
  "categories": [
    "math.PR",
    "math.CO"
  ],
  "abstract": "Given a branching random walk, let $M_n$ be the minimum position of any member of the $n$th generation. We calculate $\\mathbf{E}M_n$ to within O(1) and prove exponential tail bounds for $\\mathbf{P}\\{|M_n-\\mathbf{E}M_n|>x\\}$, under quite general conditions on the branching random walk. In particular, together with work by Bramson [Z. Wahrsch. Verw. Gebiete 45 (1978) 89--108], our results fully characterize the possible behavior of $\\mathbf {E}M_n$ when the branching random walk has bounded branching and step size.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2009-07-24T15:06:28.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60J80",
      "60G50"
    ],
    "keywords": [
      "branching random walk",
      "exponential tail bounds",
      "quite general conditions",
      "minimum position",
      "th generation"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007arXiv0712.2582A"
    }
  }
}