{
  "id": "1803.01458",
  "version": "v1",
  "published": "2018-03-05T02:01:39.000Z",
  "updated": "2018-03-05T02:01:39.000Z",
  "title": "Contact process under renewals I",
  "authors": [
    "Luiz Renato G. Fontes",
    "Domingos H. U. Marchetti",
    "Thomas S. Mountford",
    "Maria Eulalia Vares"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "Motivated by questions regarding long range percolation, we investigate a non-Markovian analogue of the Harris contact process in $\\mathbb{Z}^d$: an individual is attached to each site $x \\in \\mathbb{Z}^d$, and it can be infected or healthy; the infection propagates to healthy neighbors just as in the usual contact process, according to independent exponential times with a fixed rate $\\lambda$; nevertheless, the possible recovery times for an individual are given by the points of a renewal process with heavy tail; the renewal processes are assumed to be independent for different sites. We show that the resulting processes have a critical value equal to zero.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-03-05T02:01:39.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60K35",
      "60K05",
      "82B43"
    ],
    "keywords": [
      "renewal process",
      "questions regarding long range percolation",
      "harris contact process",
      "usual contact process",
      "independent exponential times"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}