{
  "id": "2012.04370",
  "version": "v1",
  "published": "2020-12-08T11:28:25.000Z",
  "updated": "2020-12-08T11:28:25.000Z",
  "title": "Percolation in the Boolean model with convex grains in high dimension",
  "authors": [
    "Jean-Baptiste Gouéré",
    "Florestan Labéy"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "We investigate percolation in the Boolean model with convex grains in high dimension. For each dimension d, one fixes a compact, convex and symmetric set K $\\subset$ R d with non empty interior. In a first setting, the Boolean model is a reunion of translates of K. In a second setting, the Boolean model is a reunion of translates of K or $\\rho$K for a further parameter $\\rho$ $\\in$ (1, 2). We give the asymptotic behavior of the percolation probability and of the percolation threshold in the two settings.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-12-08T11:28:25.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "boolean model",
      "convex grains",
      "high dimension",
      "non empty interior",
      "translates"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}