{
  "id": "1605.09160",
  "version": "v1",
  "published": "2016-05-30T10:05:43.000Z",
  "updated": "2016-05-30T10:05:43.000Z",
  "title": "Isotropic constant of random polytopes with vertices on an $\\ell_p$-sphere",
  "authors": [
    "Julia Hörrmann",
    "Joscha Prochno",
    "Christoph Thaele"
  ],
  "comment": "18",
  "categories": [
    "math.FA",
    "math.MG",
    "math.PR"
  ],
  "abstract": "The symmetric convex hull of random points that are independent and distributed according to the cone measure on the unit sphere of $\\ell_p^n$ for some $1\\leq p < \\infty$ is considered. We prove that these random polytopes have uniformly absolutely bounded isotropic constants with overwhelming probability. This generalizes the result for the Euclidean sphere ($p=2$) obtained by D. Alonso-Guti\\'errez. The proof requires several different tools including a concentration inequality for the cone measure due to G. Schechtman and J. Zinn and moment estimates for sums of independent random variables with log-concave tails originating in the work of E. Gluskin and S. Kwapie\\'n.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-05-30T10:05:43.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "52A20",
      "52B11",
      "60D05"
    ],
    "keywords": [
      "random polytopes",
      "cone measure",
      "symmetric convex hull",
      "independent random variables",
      "unit sphere"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}