Results related to the Gaussian product inequality conjecture for mixed-sign exponents in arbitrary dimension

2025/05/15 by Guolie Lan, Frédéric Ouimet, Lan, Guolie +3
Mathematics · #26A48 #44A10 #60E15 #62E15 #62H10 #62H12 #FOS: Mathematics #Mathematical Approximation and Integration #Point processes and geometric inequalities #Probability (math.PR) #Statistics Theory (math.ST)

paper · pdf · doi:10.48550/arxiv.2505.09976

openalex publication_date 2025/05/15 · openalex created_date 2025/10/15 · openalex updated_date 2026/08/01

Abstract

This note establishes that the opposite Gaussian product inequality (GPI) of the type proved by Russell & Sun (2022a) in two dimensions, and partially extended to higher dimensions by Zhou et al. (2024), continues to hold for an arbitrary mix of positive and negative exponents. A general quantitative lower bound is also obtained conditionally on the GPI conjecture being true.

Citations

• Some New Results on Gaussian Product Inequalities
• Moment ratio inequality of bivariate Gaussian distribution and three-dimensional Gaussian product inequality
• Quantitative Versions of the Two-dimensional Gaussian Product Inequalities
• Using Sums-of-Squares to Prove Gaussian Product Inequalities
• Product Inequalities for Multivariate Gaussian, Gamma, and Positively Upper Orthant Dependent Distributions
• The Three-Dimensional Gaussian Product Inequality
• Squared chaotic random variables: new moment inequalities with applications

Related

• An Opposite Gaussian Product Inequality
• Some New Results on Gaussian Product Inequalities
• Quantitative Versions of the Two-dimensional Gaussian Product Inequalities
• The Gaussian product inequality conjecture for multinomial covariances
• The Three-Dimensional Gaussian Product Inequality