{
  "id": "1108.5500",
  "version": "v1",
  "published": "2011-08-28T16:16:45.000Z",
  "updated": "2011-08-28T16:16:45.000Z",
  "title": "Rate of convergence of random polarizations",
  "authors": [
    "Almut Burchard"
  ],
  "comment": "5 pages",
  "categories": [
    "math.PR",
    "math.FA"
  ],
  "abstract": "After n random polarizations of Borel set on a sphere, its expected symmetric difference from a polar cap is bounded by C/n, where the constant depends on the dimension [arXiv:1104.4103]. We show here that this power law is best possible, and that the constant grows at least linearly with the dimension.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2011-08-28T16:16:45.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60D05",
      "26D15",
      "28A75",
      "52A22"
    ],
    "keywords": [
      "random polarizations",
      "convergence",
      "expected symmetric difference",
      "borel set",
      "polar cap"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 5,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1108.5500B"
    }
  }
}