Moment ratio inequality of bivariate Gaussian distribution and three-dimensional Gaussian product inequality

被引：6

作者：

Russell, Oliver ^{[1
]}

Sun, Wei ^{[1
]}

机构：

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

来源：

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2023年 / 527卷 / 01期

基金：

加拿大自然科学与工程研究理事会;

关键词：

Gaussian product inequality; conjecture; Hypergeometric function; Combinatorial inequality; Sums-of-squares; Computational mathematics; PROOF; VARIABLES;

D O I：

10.1016/j.jmaa.2023.127410

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We prove the three-dimensional Gaussian product inequality (GPI) E[X12X22m2X2m3 3] >= E[X12]E[X22m2]E[X2m3 3] for any centered Gaussian random vector (X1, X2, X3) and m2, m3 is an element of N. We discover a novel inequality for the moment ratio |E[X 2m2+1X2m3+1 2 3]| E[X22m2X2m3 3] , which implies the 3D-GPI. The interplay between computing and hard analysis plays a crucial role in the proofs. (c) 2023 Elsevier Inc. All rights reserved.

引用

页数：27

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