{
  "id": "1309.1707",
  "version": "v2",
  "published": "2013-09-06T17:48:58.000Z",
  "updated": "2015-12-31T11:20:26.000Z",
  "title": "A Gaussian correlation inequality for convex sets",
  "authors": [
    "Michael R. Tehranchi"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "A Gaussian correlation inequality is proven which generalises results of Schechtman, Schlumprecht \\& Zinn , Li and Shao. One implication of this inequality is that, for the standard Gaussian measure $\\gamma$ on $R^n$, the inequality $$ |\\sin(\\alpha + \\beta)|^n \\gamma( \\sin \\alpha \\ A) \\gamma( \\sin \\beta \\ B) \\le \\gamma( \\sin(\\alpha+\\beta) A \\cap B) \\gamma\\big( \\sin \\alpha \\sin \\beta \\ (A+B) \\big) $$ holds for all symmetric convex sets $A, B \\subseteq R^n $ and real $\\alpha, \\beta$. Furthermore, connections to the Gaussian correlation conjecture are explored.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-09-06T17:48:58.000Z",
      "abstract": "A Gaussian correlation inequality is proven which generalises results of Schechtman, Schlumprecht & Zinn, Li and Shao. Letting $\\gamma$ be the standard Gaussian measure on $R^n$, concrete implications of this inequality are that the inequality $\\gamma(A) \\gamma(B) \\le (4/3)^{n/2} \\gamma(A \\cap B)$ holds for all symmetric convex sets $A, B$, and that $\\gamma(A) \\gamma(B) \\le \\gamma(A \\cap B)$ holds for all symmetric convex subsets $A, B$ of the Euclidean unit ball of radius $0.374 \\sqrt{n}$.",
      "comment": null,
      "journal": null,
      "doi": null
    },
    {
      "version": "v2",
      "updated": "2015-12-31T11:20:26.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60E15",
      "28C20"
    ],
    "keywords": [
      "gaussian correlation inequality",
      "symmetric convex subsets",
      "symmetric convex sets",
      "standard gaussian measure",
      "euclidean unit ball"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1309.1707T"
    }
  }
}