The three-dimensional Gaussian product inequality

被引：14

作者：

Lan, Guolie ^{[1
]}

Hu, Ze-Chun ^{[2
]}

Sun, Wei ^{[3
]}

机构：

[1] Guangzhou Univ, Sch Econ & Stat, Guangzhou, Peoples R China

[2] Sichuan Univ, Coll Math, Chengdu, Peoples R China

[3] Concordia Univ, Dept Math & Stat, Montreal, PQ, Canada

来源：

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2020年 / 485卷 / 02期

基金：

中国国家自然科学基金; 加拿大自然科学与工程研究理事会;

关键词：

Moments of Gaussian randorn vector; Gaussian product conjecture; Real linear polarization constant; Hypergeometric function; VARIABLES;

D O I：

10.1016/j.jmaa.2020.123858

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We prove the 3-dimensional Gaussian product inequality, i.e., for any real-valued centered Gaussian random vector (X, Y, Z) and m is an element of N, it holds that E[X(2m)Y(2m)Z(2m)] >= E[X-2m]E[Y-2m]E[Z(2m)]. This settles positively the Gaussian product conjecture in the 3-dimensional case. Our proof is based on some improved inequalities on multi-term products involving 2-dimensional Gaussian random vectors. The improved inequalities are derived using the Gaussian hypergeometric functions and are of independent interest. As by-products, several new combinatorial identities and inequalities are obtained. (C) 2020 Elsevier Inc. All rights reserved.

引用

页数：19

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