Gaussian Correlation Inequality: Optimal Extensions
Posed by Various (post-Royen) (2014)
§ Problem Statement
Setup
Unsolved Problem
§ Discussion
§ Significance & Implications
§ References
A simple proof of the Gaussian correlation conjecture extended to multivariate gamma distributions
Thomas Royen (2014)
📍 Not stated as an open problem in Royen (2014); the paper only states the centered GCC in Section 1 (Introduction), Eq. (1.1), p. 1.
A Gaussian correlation inequality for symmetric convex sets
Loren D. Pitt (1977)
Annals of Probability
📍 Theorem 1 (GCI in dimension 2) and Conjecture on p. 473 posing the inequality for all dimensions.
Royen's proof of the Gaussian correlation inequality
Rafał Latała, Dariusz Matlak (2017)
Geometric Aspects of Functional Analysis (Lecture Notes in Mathematics, vol. 2169), Springer
📍 Section 1 (Introduction), restatement of the GCI and open questions regarding extensions to non-centered Gaussians and log-concave measures, pp. 265–266.