A note on Gaussian correlation inequalities for nonsymmetric sets

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 ${\gamma }_d(A\cap B)\ge {\gamma }_d(A){\gamma }_d(B)$, 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].

9 pages

References in corpus (1)

• On the Gaussian measure of the intersection of symmetric, convex sets

Cited by in corpus (1)

• The Gaussian Correlation Inequality for Symmetric Convex Sets