{
  "id": "1308.1506",
  "version": "v3",
  "published": "2013-08-07T08:55:54.000Z",
  "updated": "2014-11-07T09:39:14.000Z",
  "title": "Asymptotic properties of a random graph with duplications",
  "authors": [
    "Ágnes Backhausz",
    "Tamás F. Móri"
  ],
  "comment": "19 pages; results of the first version strengthened. v3: typo corrected",
  "categories": [
    "math.PR"
  ],
  "abstract": "We deal with a random graph model evolving in discrete time steps by duplicating and deleting the edges of randomly chosen vertices. We prove the existence of an a.s. asymptotic degree distribution, with streched exponential decay; more precisely, the proportion of vertices of degree $d$ tends to some positive number $c_d>0$ almost surely as the number of steps goes to infinity, and $c_d\\sim (e\\pi)^{1/2} d^{1/4} e^{-2\\sqrt d}$ holds as $d\\to\\infty$.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2013-09-02T10:29:47.000Z",
      "comment": "19 pages; results of the first version strengthened",
      "journal": null,
      "doi": null
    },
    {
      "version": "v3",
      "updated": "2014-11-07T09:39:14.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60G42",
      "05C80"
    ],
    "keywords": [
      "asymptotic properties",
      "duplications",
      "discrete time steps",
      "asymptotic degree distribution",
      "streched exponential decay"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 19,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1308.1506B"
    }
  }
}