{
  "id": "1011.4166",
  "version": "v1",
  "published": "2010-11-18T10:25:14.000Z",
  "updated": "2010-11-18T10:25:14.000Z",
  "title": "A note on Gaussian correlation inequalities for nonsymmetric sets",
  "authors": [
    "Adrian P. C. Lim",
    "Dejun Luo"
  ],
  "comment": "9 pages",
  "journal": "Statistics & Probability Letters 82 (2012), no. 1, 196--202",
  "doi": "10.1016/j.spl.2011.10.001",
  "categories": [
    "math.PR"
  ],
  "abstract": "We consider the Gaussian correlation inequality for nonsymmetric convex sets. More precisely, if $A\\subset\\mathbb{R}^d$ is convex and the origin $0\\in A$, then for any ball $B$ centered at the origin, it holds $\\gamma_d(A\\cap B)\\geq \\gamma_d(A)\\gamma_d(B)$, where $\\gamma_d$ is the standard Gaussian measure on $\\mathbb{R}^d$. This generalizes Proposition 1 in [Arch. Rational Mech. Anal. 161 (2002), 257--269].",
  "revisions": [
    {
      "version": "v1",
      "updated": "2010-11-18T10:25:14.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "gaussian correlation inequality",
      "nonsymmetric sets",
      "nonsymmetric convex sets",
      "standard gaussian measure",
      "generalizes proposition"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 9,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1011.4166L"
    }
  }
}