{
  "id": "1708.03054",
  "version": "v1",
  "published": "2017-08-10T02:19:04.000Z",
  "updated": "2017-08-10T02:19:04.000Z",
  "title": "Noise sensitivity and Voronoi percolation",
  "authors": [
    "Daniel Ahlberg",
    "Rangel Baldasso"
  ],
  "comment": "28 pages, 2 figures",
  "categories": [
    "math.PR",
    "math.CO"
  ],
  "abstract": "In this paper we study noise sensitivity and threshold phenomena for Poisson Voronoi percolation on $\\mathbb{R}^2$. In the setting of Boolean functions, both threshold phenomena and noise sensitivity can be understood via the study of randomized algorithms. Together with a simple discretization argument, such techniques apply also to the continuum setting. Via the study of a suitable algorithm we show that box-crossing events in Voronoi percolation are noise sensitive and present a threshold phenomenon with polynomial window. We also study the effect of other kinds of perturbations, and emphasize the fact that the techniques we use apply for a broad range of models.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-08-10T02:19:04.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60K35",
      "82B43",
      "60G55"
    ],
    "keywords": [
      "threshold phenomenon",
      "study noise sensitivity",
      "simple discretization argument",
      "poisson voronoi percolation",
      "broad range"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 28,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}