{
  "id": "1607.05501",
  "version": "v1",
  "published": "2016-07-19T10:03:44.000Z",
  "updated": "2016-07-19T10:03:44.000Z",
  "title": "A short proof of the asymptotic of the minimum of the branching random walk after time $n$",
  "authors": [
    "Bastien Mallein"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "We write $R_n$ for the minimal position attained after time $n$ by a branching random walk in the boundary case. In this article, we prove that $R_n - \\frac{1}{2} \\log n$ converges in law toward a shifted Gumbel distribution.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-07-19T10:03:44.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "branching random walk",
      "short proof",
      "asymptotic",
      "minimal position",
      "boundary case"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}