{
  "id": "2203.01251",
  "version": "v1",
  "published": "2022-03-02T17:16:11.000Z",
  "updated": "2022-03-02T17:16:11.000Z",
  "title": "Sharp phase transition for Cox percolation",
  "authors": [
    "Christian Hirsch",
    "Benedikt Jahnel",
    "Stephen Muirhead"
  ],
  "comment": "9 pages, 1 figure",
  "categories": [
    "math.PR"
  ],
  "abstract": "We prove the sharpness of the percolation phase transition for a class of Cox percolation models, i.e., models of continuum percolation in a random environment. The key requirements are that the environment has a finite range of dependence and satisfies a local boundedness condition, however the FKG inequality need not hold. The proof combines the OSSS inequality with a coarse-graining construction.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-03-02T17:16:11.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60F10",
      "60K35"
    ],
    "keywords": [
      "sharp phase transition",
      "cox percolation models",
      "percolation phase transition",
      "local boundedness condition",
      "osss inequality"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 9,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}