{
  "id": "2205.15366",
  "version": "v1",
  "published": "2022-05-30T18:20:13.000Z",
  "updated": "2022-05-30T18:20:13.000Z",
  "title": "Continuum Percolation in a Nonstabilizing Environment",
  "authors": [
    "Benedikt Jahnel",
    "Sanjoy Kumar Jhawar",
    "Anh Duc Vu"
  ],
  "comment": "34 pages, 12 figures",
  "categories": [
    "math.PR"
  ],
  "abstract": "We prove nontrivial phase transitions for continuum percolation in a Boolean model based on a Cox point process with nonstabilizing directing measure. The directing measure, which can be seen as a stationary random environment for the classical Poisson-Boolean model, is given by a planar rectangular Poisson line process. This Manhattan grid type construction features long-range dependencies in the environment, leading to absence of a sharp phase transition for the associated Cox-Boolean model. Our proofs rest on discretization arguments and a comparison to percolation on randomly stretched lattices established in Hoffman 2005.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-05-30T18:20:13.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60K35",
      "60K37",
      "60G55",
      "90B18"
    ],
    "keywords": [
      "continuum percolation",
      "nonstabilizing environment",
      "planar rectangular poisson line process",
      "manhattan grid type construction features",
      "grid type construction features long-range"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 34,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}