{
  "id": "0708.2513",
  "version": "v1",
  "published": "2007-08-18T23:27:48.000Z",
  "updated": "2007-08-18T23:27:48.000Z",
  "title": "Pointwise Estimates for Marginals of Convex Bodies",
  "authors": [
    "Ronen Eldan",
    "Bo'az Klartag"
  ],
  "comment": "17 pages",
  "categories": [
    "math.MG",
    "math.FA"
  ],
  "abstract": "We prove a pointwise version of the multi-dimensional central limit theorem for convex bodies. Namely, let X be an isotropic random vector in R^n with a log-concave density. For a typical subspace E in R^n of dimension n^c, consider the probability density of the projection of X onto E. We show that the ratio between this probability density and the standard gaussian density in E is very close to 1 in large parts of E. Here c > 0 is a universal constant. This complements a recent result by the second named author, where the total-variation metric between the densities was considered.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2007-08-18T23:27:48.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "convex bodies",
      "pointwise estimates",
      "multi-dimensional central limit theorem",
      "probability density",
      "isotropic random vector"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007arXiv0708.2513E"
    }
  }
}