{
  "id": "1608.02440",
  "version": "v1",
  "published": "2016-08-08T14:05:05.000Z",
  "updated": "2016-08-08T14:05:05.000Z",
  "title": "A branching random walk among disasters",
  "authors": [
    "Nina Gantert",
    "Stefan Junk"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "We consider a branching random walk in a random space-time environment of disasters where each particle is killed when meeting a disaster. This extends the model of the \"random walk in a disastrous random environment\" introduced by [6]. We obtain a criterion for positive survival probability, see Theorem 1. The proofs for the subcritical and the supercritical cases follow standard arguments, which involve moment methods and a comparison with an embedded branching process with i.i.d. offspring distributions. The proof of almost sure extinction in the critical case is more difficult and uses the techniques from [4]. We also show that, in the case of survival, the number of particles grows exponentially fast.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-08-08T14:05:05.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60K37",
      "60J80",
      "82D60"
    ],
    "keywords": [
      "branching random walk",
      "random space-time environment",
      "particles grows exponentially fast",
      "disastrous random environment",
      "positive survival probability"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}