{
  "id": "1509.08454",
  "version": "v1",
  "published": "2015-09-28T19:58:25.000Z",
  "updated": "2015-09-28T19:58:25.000Z",
  "title": "Noise sensitivity in bootstrap percolation",
  "authors": [
    "Zsolt Bartha",
    "Gábor Pete"
  ],
  "comment": "16 pages",
  "categories": [
    "math.PR",
    "math.CO"
  ],
  "abstract": "Answering questions of Itai Benjamini, we show that the event of complete occupation in 2-neighbour bootstrap percolation on the d-dimensional box [n]^d, for d\\geq 2, at its critical initial density p_c(n), is noise sensitive, while in k-neighbour bootstrap percolation on the d-regular random graph G_{n,d}, for 2\\leq k\\leq d-2, it is insensitive. Many open problems remain.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-09-28T19:58:25.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "noise sensitivity",
      "open problems remain",
      "d-regular random graph",
      "k-neighbour bootstrap percolation",
      "itai benjamini"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 16,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150908454B"
    }
  }
}