{
  "id": "2003.12813",
  "version": "v1",
  "published": "2020-03-28T15:17:28.000Z",
  "updated": "2020-03-28T15:17:28.000Z",
  "title": "The Constrained-degree percolation model",
  "authors": [
    "Bernardo N. B. de Lima",
    "Rémy Sanchis",
    "Diogo C. dos Santos",
    "Vladas Sidoravicius",
    "Roberto Teodoro"
  ],
  "comment": "22 pages, 5 figures. To appear in Stochastic Processes and their Applications",
  "categories": [
    "math.PR"
  ],
  "abstract": "In the Constrained-degree percolation model on a graph $(\\mathbb{V},\\mathbb{E})$ there are a sequence, $(U_e)_{e\\in\\mathbb{E}}$, of i.i.d. random variables with distribution $U[0,1]$ and a positive integer $k$. Each bond $e$ tries to open at time $U_e$, it succeeds if both its end-vertices would have degrees at most $k-1$. We prove a phase transition theorem for this model on the square lattice $\\mathbb{L}^2$, as well as on the d-ary regular tree. We also prove that on the square lattice the infinite cluster is unique in the supercritical phase.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-03-28T15:17:28.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60K35",
      "82B43"
    ],
    "keywords": [
      "constrained-degree percolation model",
      "square lattice",
      "d-ary regular tree",
      "phase transition theorem",
      "random variables"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 22,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}