{
  "id": "1711.07768",
  "version": "v1",
  "published": "2017-11-21T13:21:18.000Z",
  "updated": "2017-11-21T13:21:18.000Z",
  "title": "Localisation in a growth model with interaction",
  "authors": [
    "Marcelo Costa",
    "Mikhail Menshikov",
    "Vadim Shcherbakov",
    "Marina Vachkovskaia"
  ],
  "comment": "31 pages, 2 figures",
  "categories": [
    "math.PR"
  ],
  "abstract": "This paper concerns the long term behaviour of a growth model describing a random sequential allocation of particles on a finite cycle graph. The model can be regarded as a reinforced urn model with graph-based interactions. It is motivated by cooperative sequential adsorption, where adsorption rates at a site depend on the configuration of existing particles in the neighbourhood of that site. Our main result is that, with probability one, the growth process will eventually localise either at a single site, or at a pair of neighbouring sites.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-11-21T13:21:18.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "growth model",
      "interaction",
      "localisation",
      "long term behaviour",
      "random sequential allocation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 31,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}