{
  "id": "math/0501481",
  "version": "v2",
  "published": "2005-01-27T20:56:09.000Z",
  "updated": "2005-07-14T22:03:23.000Z",
  "title": "Two Phase Transitions for the Contact Process on Small Worlds",
  "authors": [
    "Rick Durrett",
    "Paul Jung"
  ],
  "comment": "24 pages, 6 figures. We have rewritten the phase transition in terms of two parameters and have made improvements to our original results",
  "categories": [
    "math.PR"
  ],
  "abstract": "In our version of Watts and Strogatz's small world model, space is a d-dimensional torus in which each individual has in addition exactly one long-range neighbor chosen at random from the grid. This modification is natural if one thinks of a town where an individual's interactions at school, at work, or in social situations introduces long-range connections. However, this change dramatically alters the behavior of the contact process, producing two phase transitions. We establish this by relating the small world to an infinite \"big world\" graph where the contact process behavior is similar to the contact process on a tree.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2005-07-14T22:03:23.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60K35"
    ],
    "keywords": [
      "phase transitions",
      "strogatzs small world model",
      "long-range neighbor chosen",
      "contact process behavior",
      "individuals interactions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 24,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2005math......1481D"
    }
  }
}