{
  "id": "math/0610192",
  "version": "v1",
  "published": "2006-10-05T14:29:17.000Z",
  "updated": "2006-10-05T14:29:17.000Z",
  "title": "Central limit theorems for Gaussian polytopes",
  "authors": [
    "I. Barany",
    "V. H. Vu"
  ],
  "comment": "to appear in Annals of Probability",
  "categories": [
    "math.CO",
    "math.PR"
  ],
  "abstract": "Choose $n$ random, independent points in $\\R^d$ according to the standard normal distribution. Their convex hull $K_n$ is the {\\sl Gaussian random polytope}. We prove that the volume and the number of faces of $K_n$ satisfy the central limit theorem, settling a well known conjecture in the field.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2006-10-05T14:29:17.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "central limit theorem",
      "gaussian polytopes",
      "standard normal distribution",
      "gaussian random polytope",
      "convex hull"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math.....10192B"
    }
  }
}