{
  "id": "1908.09498",
  "version": "v1",
  "published": "2019-08-26T07:13:33.000Z",
  "updated": "2019-08-26T07:13:33.000Z",
  "title": "Poisson hyperplane processes and approximation of convex bodies",
  "authors": [
    "Daniel Hug",
    "Rolf Schneider"
  ],
  "categories": [
    "math.PR",
    "math.MG"
  ],
  "abstract": "A natural model for the approximation of a convex body $K$ in $\\mathbb{R}^d$ by random polytopes is obtained as follows. Take a stationary Poisson hyperplane process in the space, and consider the random polytope $Z_K$ defined as the intersection of all closed halfspaces containing $K$ that are bounded by hyperplanes of the process not intersecting $K$. If $f$ is a functional on convex bodies, then for increasing intensities of the process, the expectation of the difference $f(Z_K)-f(K)$ may or may not converge to zero. If it does, then the order of convergence and possible limit relations are of interest. We study these questions if $f$ is either the hitting functional or the mean width.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-08-26T07:13:33.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60D05",
      "52A27"
    ],
    "keywords": [
      "convex body",
      "approximation",
      "stationary poisson hyperplane process",
      "random polytope",
      "natural model"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}