{
  "id": "1111.6466",
  "version": "v2",
  "published": "2011-11-28T15:11:56.000Z",
  "updated": "2011-12-23T16:26:01.000Z",
  "title": "A Central Limit Theorem for the Poisson-Voronoi Approximation",
  "authors": [
    "Matthias Schulte"
  ],
  "comment": "22 pages, modified references",
  "categories": [
    "math.PR",
    "math.MG"
  ],
  "abstract": "For a compact convex set $K$ and a Poisson point process $\\eta$, the union of all Voronoi cells with a nucleus in $K$ is the Poisson-Voronoi approximation of $K$. Lower and upper bounds for the variance and a central limit theorem for the volume of the Poisson-Voronoi approximation are shown. The proofs make use of so called Wiener-It\\^o chaos expansions and the central limit theorem is based on a more abstract central limit theorem for Poisson functionals, which is also derived.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2011-12-23T16:26:01.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60D05",
      "60F05",
      "60G55",
      "60H07"
    ],
    "keywords": [
      "poisson-voronoi approximation",
      "abstract central limit theorem",
      "compact convex set",
      "poisson point process",
      "poisson functionals"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 22,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1111.6466S"
    }
  }
}