{
  "id": "1903.04418",
  "version": "v1",
  "published": "2019-03-11T16:29:42.000Z",
  "updated": "2019-03-11T16:29:42.000Z",
  "title": "Localisation in a growth model with interaction. Arbitrary graphs",
  "authors": [
    "Mikhail Menshikov",
    "Vadim Shcherbakov"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "This paper concerns the long term behaviour of a growth model describing a random sequential deposition of particles on a finite graph. The probability of allocating a particle at a vertex is proportional to a log-linear function of numbers of existing particles in a neighbourhood of a vertex. When this function depends only on the number of particles in the vertex, the model becomes a special case of the generalised Polya urn model. In this special case all but finitely many particles are allocated at a single random vertex almost surely. In our model interaction leads to the fact that, with probability one, all but finitely many particles are allocated at vertices of a clique.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-03-11T16:29:42.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "growth model",
      "arbitrary graphs",
      "interaction",
      "localisation",
      "special case"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}