Quantitative versions of the two-dimensional Gaussian product inequalities

Article Mathematics, Applied

Miscellaneous results related to the Gaussian product inequality conjecture for the joint distribution of traces of Wishart matrices

Christian Genest et al.

Summary: This note presents partial results on the Gaussian product inequality (GPI) conjecture for the joint distribution of traces of Wishart matrices. It extends several GPI-related results from Wei [32] and Liu et al. [15] by replacing power functions with more general classes of functions and by replacing the usual Gaussian and multivariate gamma distributional assumptions with the more general trace-Wishart distribution assumption. These findings suggest that a Kronecker product form of the GPI holds for diagonal blocks of any Wishart distribution.

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS (2023)

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Article Statistics & Probability

Quantitative correlation inequalities via extremal power series

Anindya De et al.

Summary: In this paper, by using tools from complex analysis and a new extremal bound on power series, the authors obtain new and near-optimal quantitative correlation inequalities. These include a quantitative version of Royen's celebrated Gaussian Correlation Inequality and a quantitative version of the FKG inequality for monotone functions over any finite product probability space.

PROBABILITY THEORY AND RELATED FIELDS (2022)

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Article Statistics & Probability

An opposite Gaussian product inequality

Oliver Russell et al.

Summary: In this note, we prove a novel opposite Gaussian product inequality for specific bivariate Gaussian random variables. This finding completes the theory of bivariate Gaussian product relations.

STATISTICS & PROBABILITY LETTERS (2022)

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Article Mathematics, Applied

Some new Gaussian product inequalities

Oliver Russell et al.

Summary: This paper investigates a long-standing Gaussian product inequality and derives some novel moment inequalities through the derivation of combinatorial inequalities and the Cauchy-Schwarz inequality.

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS (2022)

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Article Statistics & Probability

A combinatorial proof of the Gaussian product inequality beyond the MTP2 case

Christian Genest et al.

Summary: This article provides a combinatorial proof of the Gaussian product inequality (GPI) by utilizing the characteristics of centered Gaussian random vectors and the monotonicity of a certain ratio of gamma functions.

DEPENDENCE MODELING (2022)

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Article Mathematics, Applied