{
  "id": "1508.06267",
  "version": "v1",
  "published": "2015-08-25T19:52:57.000Z",
  "updated": "2015-08-25T19:52:57.000Z",
  "title": "Nucleation and growth in two dimensions",
  "authors": [
    "Béla Bollobás",
    "Simon Griffiths",
    "Robert Morris",
    "Leonardo Rolla",
    "Paul Smith"
  ],
  "comment": "34 pages",
  "categories": [
    "math.PR",
    "math.CO"
  ],
  "abstract": "We consider a dynamical process on a graph $G$, in which vertices are infected (randomly) at a rate which depends on the number of their neighbours that are already infected. This model includes bootstrap percolation and first-passage percolation as its extreme points. We give a precise description of the evolution of this process on the graph $\\mathbb{Z}^2$, significantly sharpening results of Dehghanpour and Schonmann. In particular, we determine the typical infection time up to a constant factor for almost all natural values of the parameters, and in a large range we obtain a stronger, sharp threshold.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-08-25T19:52:57.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "nucleation",
      "dimensions",
      "bootstrap percolation",
      "first-passage percolation",
      "extreme points"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 34,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150806267B"
    }
  }
}