The Annals of Probability

A Gaussian Correlation Inequality for Symmetric Convex Sets

Loren D. Pitt

Full-text: Open access

Abstract

If $n(x)$ is the standard normal density on $R^2$ and if $A = -A$ and $B = -B$ are convex subsets of $R^2$ then $$\int_{A\cap B}\mathbf{n}(x) d^2x \geqq (\int_A \mathbf{n}(x) d^2x)(\int_B \mathbf{n}(x) d^2x).$$

Article information

Source
Ann. Probab. Volume 5, Number 3 (1977), 470-474.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
http://projecteuclid.org/euclid.aop/1176995808

Digital Object Identifier
doi:10.1214/aop/1176995808

Mathematical Reviews number (MathSciNet)
MR448705

Zentralblatt MATH identifier
0359.60018

JSTOR
links.jstor.org

Subjects
Primary: 60G15: Gaussian processes
Secondary: 26A51: Convexity, generalizations

Keywords
Quasi-concave functions convex sets correlation inequalities

Citation

Pitt, Loren D. A Gaussian Correlation Inequality for Symmetric Convex Sets. Ann. Probab. 5 (1977), no. 3, 470--474. doi:10.1214/aop/1176995808. http://projecteuclid.org/euclid.aop/1176995808.


Export citation