{
  "id": "1607.06610",
  "version": "v1",
  "published": "2016-07-22T09:30:16.000Z",
  "updated": "2016-07-22T09:30:16.000Z",
  "title": "On the genealogy of branching random walks and of directed polymers",
  "authors": [
    "Bernard Derrida",
    "Peter Mottishaw"
  ],
  "comment": "7 pages, 3 figures, submitted to EPL",
  "categories": [
    "cond-mat.stat-mech",
    "cond-mat.dis-nn"
  ],
  "abstract": "It is well known that the mean field theory of directed polymers in a random medium exhibits replica symmetry breaking with a distribution of overlaps which consists of two delta functions. Here we show that the leading finite size correction to this distribution of overlaps has a universal character which can be computed explicitly. Our results can also be interpreted as genealogical properties of branching Brownian motion or of branching random walks.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-07-22T09:30:16.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "branching random walks",
      "directed polymers",
      "mean field theory",
      "branching brownian motion",
      "universal character"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 7,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}