{
  "id": "1704.07144",
  "version": "v1",
  "published": "2017-04-24T11:03:43.000Z",
  "updated": "2017-04-24T11:03:43.000Z",
  "title": "Bootstrap percolation in random $k$-uniform hypergraphs",
  "authors": [
    "Mihyun Kang",
    "Christoph Koch",
    "Tamás Makai"
  ],
  "comment": "Extended abstract presented at the European Conference on Combinatorics, Graph Theory and Applications 2015",
  "journal": "Electronic Notes in Discrete Mathematics 49 (2015) 595-601",
  "doi": "10.1016/j.endm.2015.06.081",
  "categories": [
    "math.CO",
    "math.PR"
  ],
  "abstract": "We investigate bootstrap percolation with infection threshold $r> 1$ on the binomial $k$-uniform random hypergraph $H_k(n,p)$ in the regime $n^{-1}\\ll n^{k-2}p \\ll n^{-1/r}$, when the initial set of infected vertices is chosen uniformly at random from all sets of given size. We establish a threshold such that if there are less vertices in the initial set of infected vertices, then whp only a few additional vertices become infected, while if the initial set of infected vertices exceeds the threshold then whp almost every vertex becomes infected. In addition, for $k=2$, we show that the probability of failure decreases exponentially.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-04-24T11:03:43.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "bootstrap percolation",
      "uniform hypergraphs",
      "initial set",
      "uniform random hypergraph",
      "infection threshold"
    ],
    "tags": [
      "conference paper",
      "journal article"
    ],
    "publication": {
      "publisher": "Elsevier"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}