{
  "id": "1601.01656",
  "version": "v1",
  "published": "2016-01-07T20:19:30.000Z",
  "updated": "2016-01-07T20:19:30.000Z",
  "title": "Branching Random Walks, Stable Point Processes and Regular Variation",
  "authors": [
    "Ayan Bhattacharya",
    "Rajat Subhra Hazra",
    "Parthanil Roy"
  ],
  "comment": "30 pages. 2 figures",
  "categories": [
    "math.PR"
  ],
  "abstract": "Using the language of regular variation, we give a sufficient condition for a point process to be in the superposition domain of attraction of a strictly stable point process. This sufficient condition is then used to obtain an explicit representation of the weak limit of a sequence of point processes induced by a branching random walk with jointly regularly varying displacements. As a consequence, we extend the main result of Durrett (1983) and verify that two related predictions of Brunet and Derrida (2011) remain valid for this model.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-01-07T20:19:30.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60J70",
      "60G55",
      "60J80"
    ],
    "keywords": [
      "branching random walk",
      "regular variation",
      "sufficient condition",
      "explicit representation",
      "strictly stable point process"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 30,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2016arXiv160101656B"
    }
  }
}