{
  "id": "2006.01323",
  "version": "v1",
  "published": "2020-06-02T00:29:06.000Z",
  "updated": "2020-06-02T00:29:06.000Z",
  "title": "Intersections of random sets",
  "authors": [
    "Jacob Richey",
    "Amites Sarkar"
  ],
  "comment": "30 pages, 2 figures",
  "categories": [
    "math.PR"
  ],
  "abstract": "We consider a variant of a classical coverage process, the boolean model in $\\mathbb{R}^d$. Previous efforts have focused on convergence of the unoccupied region containing the origin to a well studied limit $C$. We study the intersection of sets centered at points of a Poisson point process confined to the unit ball. Using a coupling between the intersection model and the original boolean model, we show that the scaled intersection converges weakly to the same limit $C$. Along the way, we present some tools for studying statistics of a class of intersection models.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-06-02T00:29:06.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "random sets",
      "intersection model",
      "poisson point process",
      "original boolean model",
      "unit ball"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 30,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}