{
  "id": "1908.02112",
  "version": "v1",
  "published": "2019-08-06T12:47:30.000Z",
  "updated": "2019-08-06T12:47:30.000Z",
  "title": "Concentration inequalities for functionals of Poisson cylinder processes",
  "authors": [
    "Anastas Baci",
    "Carina Betken",
    "Anna Gusakova",
    "Christoph Thaele"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "Random union sets $Z$ associated with stationary Poisson processes of $k$-cylinders in $\\mathbb{R}^d$ are considered. Under general conditions on the typical cylinder base a concentration inequality for the volume of $Z$ restricted to a compact window is derived. Assuming convexity of the typical cylinder base and isotropy of $Z$ a concentration inequality for intrinsic volumes of arbitrary order is established. A number of special cases are discussed, for example the case when the cylinder bases arise from a random rotation of a fixed convex body. Also the situation of expanding windows is studied. Special attention is payed to the case $k=0$, which corresponds to the classical Boolean model.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-08-06T12:47:30.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60D05",
      "60F10",
      "52A22",
      "60E15"
    ],
    "keywords": [
      "concentration inequality",
      "poisson cylinder processes",
      "typical cylinder base",
      "functionals",
      "random union sets"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}