{
  "id": "1302.3385",
  "version": "v1",
  "published": "2013-02-14T12:27:34.000Z",
  "updated": "2013-02-14T12:27:34.000Z",
  "title": "Robust analysis of preferential attachment models with fitness",
  "authors": [
    "Steffen Dereich",
    "Marcel Ortgiese"
  ],
  "comment": "22 pages",
  "doi": "10.1017/S0963548314000157",
  "categories": [
    "math.PR"
  ],
  "abstract": "The preferential attachment network with fitness is a dynamic random graph model. New vertices are introduced consecutively and a new vertex is attached to an old vertex with probability proportional to the degree of the old one multiplied by a random fitness. We concentrate on the typical behaviour of the graph by calculating the fitness distribution of a vertex chosen proportional to its degree. For a particular variant of the model, this analysis was first carried out by Borgs, Chayes, Daskalakis and Roch. However, we present a new method, which is robust in the sense that it does not depend on the exact specification of the attachment law. In particular, we show that a peculiar phenomenon, referred to as Bose-Einstein condensation, can be observed in a wide variety of models. Finally, we also compute the joint degree and fitness distribution of a uniformly chosen vertex.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-02-14T12:27:34.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C80",
      "60G42",
      "90B15"
    ],
    "keywords": [
      "preferential attachment models",
      "robust analysis",
      "fitness distribution",
      "dynamic random graph model",
      "preferential attachment network"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 22,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1302.3385D"
    }
  }
}