The Gaussian Correlation Inequality for Symmetric Convex Sets

2010/12/03 by Qingyang, Guan · 1 citation
Mathematics · #60E15 #FOS: Mathematics #Functional Equations Stability Results #Mathematical Inequalities and Applications #Point processes and geometric inequalities #Primary 60G15 #Probability (math.PR) #Secondary 28C20

paper · pdf · doi:10.48550/arxiv.1012.0676

openalex publication_date 2010/12/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• Classes of orderings of measures and related correlation inequalities. I. Multivariate totally positive distributions

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