{
  "id": "1405.5449",
  "version": "v3",
  "published": "2014-05-21T15:08:01.000Z",
  "updated": "2016-06-06T05:54:23.000Z",
  "title": "Intermittency for branching random walk in Pareto environment",
  "authors": [
    "Marcel Ortgiese",
    "Matthew I. Roberts"
  ],
  "comment": "Published at http://dx.doi.org/10.1214/15-AOP1021 in the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org)",
  "journal": "Annals of Probability 2016, Vol. 44, No. 3, 2198-2263",
  "doi": "10.1214/15-AOP1021",
  "categories": [
    "math.PR"
  ],
  "abstract": "We consider a branching random walk on the lattice, where the branching rates are given by an i.i.d. Pareto random potential. We describe the process, including a detailed shape theorem, in terms of a system of growing lilypads. As an application we show that the branching random walk is intermittent, in the sense that most particles are concentrated on one very small island with large potential. Moreover, we compare the branching random walk to the parabolic Anderson model and observe that although the two systems show similarities, the mechanisms that control the growth are fundamentally different.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2014-05-22T07:48:51.000Z",
      "title": "Intermittency for branching random walk in heavy tailed environment",
      "comment": "59 pages, 11 figures",
      "journal": null,
      "doi": null
    },
    {
      "version": "v3",
      "updated": "2016-06-06T05:54:23.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60K37",
      "60J80"
    ],
    "keywords": [
      "branching random walk",
      "heavy tailed environment",
      "intermittency",
      "parabolic anderson model",
      "pareto random potential"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 59,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1405.5449O"
    }
  }
}