{
  "id": "1309.3989",
  "version": "v2",
  "published": "2013-09-16T15:02:04.000Z",
  "updated": "2013-12-16T15:02:25.000Z",
  "title": "Approximation properties of random polytopes associated with Poisson hyperplane processes",
  "authors": [
    "Daniel Hug",
    "Rolf Schneider"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "We consider a stationary Poisson hyperplane process with given directional distribution and intensity in $d$-dimensional Euclidean space. Generalizing the zero cell of such a process, we fix a convex body $K$ and consider the intersection of all closed halfspaces bounded by hyperplanes of the process and containing $K$. We study how well these random polytopes approximate $K$ (measured by the Hausdorff distance) if the intensity increases, and how this approximation depends on the directional distribution in relation to properties of $K$.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2013-12-16T15:02:25.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60D05"
    ],
    "keywords": [
      "poisson hyperplane processes",
      "random polytopes",
      "approximation properties",
      "stationary poisson hyperplane process",
      "directional distribution"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1309.3989H"
    }
  }
}