{
  "id": "1305.6201",
  "version": "v2",
  "published": "2013-05-27T12:56:38.000Z",
  "updated": "2015-06-24T11:54:23.000Z",
  "title": "Maximal displacement in a branching random walk through interfaces",
  "authors": [
    "Bastien Mallein"
  ],
  "comment": "42 pages, 7 figures, published in EJP",
  "journal": "Electron. J. Probab. 20 (2015), no. 68, 1--40",
  "doi": "10.1214/EJP.v20-2828",
  "categories": [
    "math.PR"
  ],
  "abstract": "In this article, we study a branching random walk in an environment which depends on the time. This time-inhomogeneous environment consists of a sequence of macroscopic time intervals, in each of which the law of reproduction remains constant. We prove that the asymptotic behaviour of the maximal displacement in this process consists of a first ballistic order, given by the solution of an optimization problem under constraints, a negative logarithmic correction, plus stochastically bounded fluctuations.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-05-27T12:56:38.000Z",
      "title": "Position of the rightmost individual in a branching random walk through an interface",
      "abstract": "We study the maximal displacement of a branching random walk in a time-inhomogeneous environment, which consists of two macroscopic stages with different branching mechanisms. The study of the different asymptotics of this maximum, up to a stochastically bounded term, shows that the first order (ballistic) is given by the solution of an optimisation problem under constraints. The second order, a logarithmic correction, exhibits a phase transition.",
      "comment": "24 pages",
      "journal": null,
      "doi": null
    },
    {
      "version": "v2",
      "updated": "2015-06-24T11:54:23.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60J80",
      "60G50"
    ],
    "keywords": [
      "branching random walk",
      "rightmost individual",
      "maximal displacement",
      "macroscopic stages",
      "phase transition"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 42,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1305.6201M"
    }
  }
}