{
  "id": "1802.01847",
  "version": "v1",
  "published": "2018-02-06T08:59:24.000Z",
  "updated": "2018-02-06T08:59:24.000Z",
  "title": "A large deviation approach to super-critical bootstrap percolation on the random graph $G_{n,p}$",
  "authors": [
    "Giovanni Luca Torrisi",
    "Michele Garetto",
    "Emilio Leonardi"
  ],
  "comment": "44 pages",
  "categories": [
    "math.PR",
    "cs.PF"
  ],
  "abstract": "We consider the Erd\\\"{o}s--R\\'{e}nyi random graph $G_{n,p}$ and we analyze the simple irreversible epidemic process on the graph, known in the literature as bootstrap percolation. We give a quantitative version of some results by Janson et al. (2012), providing a fine asymptotic analysis of the final size $A_n^*$ of active nodes, under a suitable super-critical regime. More specifically, we establish large deviation principles for the sequence of random variables $\\{\\frac{n- A_n^*}{f(n)}\\}_{n\\geq 1}$ with explicit rate functions and allowing the scaling function $f$ to vary in the widest possible range.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-02-06T08:59:24.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C80",
      "60K35",
      "60F10"
    ],
    "keywords": [
      "large deviation approach",
      "super-critical bootstrap percolation",
      "random graph",
      "simple irreversible epidemic process",
      "explicit rate functions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 44,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}