{
  "id": "1006.1266",
  "version": "v2",
  "published": "2010-06-07T14:30:38.000Z",
  "updated": "2010-06-10T23:41:11.000Z",
  "title": "Weak convergence for the minimal position in a branching random walk: a simple proof",
  "authors": [
    "Elie Aidekon",
    "Zhan Shi"
  ],
  "comment": "corrected reference in introduction",
  "journal": "Period. Math. Hungar. (special issue in honour of E. Cs\\'aki and P.R\\'ev\\'esz) (2010), 61,43-54",
  "categories": [
    "math.PR"
  ],
  "abstract": "Consider the boundary case in a one-dimensional super-critical branching random walk. It is known that upon the survival of the system, the minimal position after $n$ steps behaves in probability like ${3\\over 2} \\log n$ when $n\\to \\infty$. We give a simple and self-contained proof of this result, based exclusively on elementary properties of sums of i.i.d. real-valued random variables.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2010-06-10T23:41:11.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60J80"
    ],
    "keywords": [
      "minimal position",
      "weak convergence",
      "simple proof",
      "one-dimensional super-critical branching random walk",
      "boundary case"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1006.1266A"
    }
  }
}