{
  "id": "1510.07284",
  "version": "v1",
  "published": "2015-10-25T18:49:20.000Z",
  "updated": "2015-10-25T18:49:20.000Z",
  "title": "Random version of Dvoretzky's theorem in $\\ell_p^n$",
  "authors": [
    "Grigoris Paouris",
    "Petros Valettas",
    "Joel Zinn"
  ],
  "comment": "45 pages",
  "categories": [
    "math.FA"
  ],
  "abstract": "We study the dependence on $\\varepsilon$ in the critical dimension $k(n, p, \\varepsilon)$ that one can find random sections of the $\\ell_p^n$-ball which are $(1+\\varepsilon)$-spherical. For any fixed $n$ we give lower estimates for $k(n, p, \\varepsilon)$ for all eligible values $p$ and $\\varepsilon$, which agree with the sharp estimates for the extreme values $p = 1$ and $p = \\infty$. In order to do so, we provide bounds for the gaussian concentration of the $\\ell_p$-norm.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-10-25T18:49:20.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "46B06",
      "46B07",
      "46B09"
    ],
    "keywords": [
      "dvoretzkys theorem",
      "random version",
      "gaussian concentration",
      "extreme values",
      "sharp estimates"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 45,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv151007284P"
    }
  }
}