{
  "id": "1108.0310",
  "version": "v2",
  "published": "2011-08-01T13:32:15.000Z",
  "updated": "2013-05-23T21:51:22.000Z",
  "title": "Noise Sensitivity in Continuum Percolation",
  "authors": [
    "Daniel Ahlberg",
    "Erik Broman",
    "Simon Griffiths",
    "Robert Morris"
  ],
  "comment": "42 pages",
  "categories": [
    "math.PR",
    "math.CO"
  ],
  "abstract": "We prove that the Poisson Boolean model, also known as the Gilbert disc model, is noise sensitive at criticality. This is the first such result for a Continuum Percolation model, and the first for which the critical probability p_c \\ne 1/2. Our proof uses a version of the Benjamini-Kalai-Schramm Theorem for biased product measures. A quantitative version of this result was recently proved by Keller and Kindler. We give a simple deduction of the non-quantitative result from the unbiased version. We also develop a quite general method of approximating Continuum Percolation models by discrete models with p_c bounded away from zero; this method is based on an extremal result on non-uniform hypergraphs.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2013-05-23T21:51:22.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "noise sensitivity",
      "approximating continuum percolation models",
      "poisson boolean model",
      "quite general method",
      "gilbert disc model"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 42,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1108.0310A"
    }
  }
}