{
  "id": "1907.00290",
  "version": "v1",
  "published": "2019-06-29T22:44:14.000Z",
  "updated": "2019-06-29T22:44:14.000Z",
  "title": "Contact Process under heavy-tailed renewals on finite graphs",
  "authors": [
    "Luiz Renato Fontes",
    "Pablo Almeida Gomes",
    "Remy Sanchis"
  ],
  "comment": "16 pages",
  "categories": [
    "math.PR"
  ],
  "abstract": "We investigate a non-Markovian analogue of the Harris contact process in a finite connected graph G=(V,E): an individual is attached to each site x in V, 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>0; however, the recovery times for an individual are given by the points of a renewal process attached to its timeline, whose waiting times have distribution mu such that mu(t,infty) = t^{-alpha}L(t), where 1/2 < alpha < 1 and L is a slowly varying function; the renewal processes are assumed to be independent for different sites. We show that, starting with a single infected individual, if |V| < 2 + (2 alpha -1)/[(1-alpha)(2-alpha)], then the infection does not survive for any lambda; and if |V| > 1/(1-alpha), then, for every lambda, the infection has positive probability to survive",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-06-29T22:44:14.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60K35",
      "82B43"
    ],
    "keywords": [
      "finite graphs",
      "heavy-tailed renewals",
      "independent exponential times",
      "harris contact process",
      "usual contact process"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 16,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}