The Gaussian Correlation Inequality for Symmetric Convex Sets

Abstract

The paper is to prove the Gaussian correlation conjecture stating that, under the standard Gaussian measure, the measure of the intersection of any two symmetric convex sets is greater than or equal to the product of their measures. Characterization of the equality and some applications are given.

55 pages, to replace the previous versions

References in corpus (1)

• A note on Gaussian correlation inequalities for nonsymmetric sets

Cited by in corpus (3)

• Royen's proof of the Gaussian correlation inequality
• A simple proof of the Gaussian correlation conjecture extended to multivariate gamma distributions
• Inequalities for the Gaussian measure of convex sets