{
  "id": "0905.0437",
  "version": "v1",
  "published": "2009-05-04T17:48:40.000Z",
  "updated": "2009-05-04T17:48:40.000Z",
  "title": "Susceptibility in inhomogeneous random graphs",
  "authors": [
    "Svante Janson",
    "Oliver Riordan"
  ],
  "comment": "51 pages",
  "journal": "Electronic J. Combinatorics 19 (2012), P31 (59 pages)",
  "categories": [
    "math.PR",
    "math.CO"
  ],
  "abstract": "We study the susceptibility, i.e., the mean size of the component containing a random vertex, in a general model of inhomogeneous random graphs. This is one of the fundamental quantities associated to (percolation) phase transitions; in practice one of its main uses is that it often gives a way of determining the critical point by solving certain linear equations. Here we relate the susceptibility of suitable random graphs to a quantity associated to the corresponding branching process, and study both quantities in various natural examples.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2009-05-04T17:48:40.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C80",
      "60C05"
    ],
    "keywords": [
      "inhomogeneous random graphs",
      "susceptibility",
      "natural examples",
      "phase transitions",
      "random vertex"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 51,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0905.0437J"
    }
  }
}