{
  "id": "math/0503559",
  "version": "v1",
  "published": "2005-03-24T18:51:55.000Z",
  "updated": "2005-03-24T18:51:55.000Z",
  "title": "Central limit theorems for random polytopes in a smooth convex set",
  "authors": [
    "Van Vu"
  ],
  "comment": "23 pages, no figure",
  "categories": [
    "math.PR",
    "math.CO"
  ],
  "abstract": "Let $K$ be a smooth convex set with volume one in $\\BBR^d$. Choose $n$ random points in $K$ independently according to the uniform distribution. The convex hull of these points, denoted by $K_n$, is called a {\\it random polytope}. We prove that several key functionals of $K_n$ satisfy the central limit theorem as $n$ tends to infinity.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2005-03-24T18:51:55.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60D05",
      "52A22",
      "42A61"
    ],
    "keywords": [
      "smooth convex set",
      "central limit theorem",
      "random polytope",
      "convex hull",
      "uniform distribution"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 23,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2005math......3559V"
    }
  }
}