{
  "id": "math/0503650",
  "version": "v1",
  "published": "2005-03-29T06:18:35.000Z",
  "updated": "2005-03-29T06:18:35.000Z",
  "title": "A probabilistic approach to the geometry of the \\ell_p^n-ball",
  "authors": [
    "Franck Barthe",
    "Olivier Guedon",
    "Shahar Mendelson",
    "Assaf Naor"
  ],
  "comment": "Published at http://dx.doi.org/10.1214/009117904000000874 in the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org)",
  "journal": "Annals of Probability 2005, Vol. 33, No. 2, 480-513",
  "doi": "10.1214/009117904000000874",
  "categories": [
    "math.PR"
  ],
  "abstract": "This article investigates, by probabilistic methods, various geometric questions on B_p^n, the unit ball of \\ell_p^n. We propose realizations in terms of independent random variables of several distributions on B_p^n, including the normalized volume measure. These representations allow us to unify and extend the known results of the sub-independence of coordinate slabs in B_p^n. As another application, we compute moments of linear functionals on B_p^n, which gives sharp constants in Khinchine's inequalities on B_p^n and determines the \\psi_2-constant of all directions on B_p^n. We also study the extremal values of several Gaussian averages on sections of B_p^n (including mean width and \\ell-norm), and derive several monotonicity results as p varies. Applications to balancing vectors in \\ell_2 and to covering numbers of polyhedra complete the exposition.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2005-03-29T06:18:35.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60E15",
      "52A20",
      "52A38",
      "52A40"
    ],
    "keywords": [
      "probabilistic approach",
      "independent random variables",
      "probabilistic methods",
      "monotonicity results",
      "mean width"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2005math......3650B"
    }
  }
}