{
  "id": "1705.02277",
  "version": "v1",
  "published": "2017-05-05T15:52:37.000Z",
  "updated": "2017-05-05T15:52:37.000Z",
  "title": "Slower deviations of the branching Brownian motion and of branching random walks",
  "authors": [
    "Bernard Derrida",
    "Zhan Shi"
  ],
  "comment": "13 pages and 1 figure",
  "categories": [
    "math-ph",
    "cond-mat.stat-mech",
    "math.MP",
    "math.PR"
  ],
  "abstract": "We have shown recently how to calculate the large deviation function of the position $X_{\\max}(t) $ of the right most particle of a branching Brownian motion at time $t$. This large deviation function exhibits a phase transition at a certain negative velocity. Here we extend this result to more general branching random walks and show that the probability distribution of $X_{\\max}(t)$ has, asymptotically in time, a prefactor characterized by non trivial power law.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-05-05T15:52:37.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "branching brownian motion",
      "slower deviations",
      "large deviation function",
      "non trivial power law",
      "general branching random walks"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}