四川大学学报（自然科学版）2021，Vol.58Issue(6)：15-21,7.DOI:10.19907/j.0490-6756.2021.061003
关于高斯最小值猜测的一个注记
A note on the Gaussian minimum conjecture
摘要
Abstract
Gaussian distribution,also called normal distribution,plays an important role in mathematics,statistics,physics,engineering,etc.Inequalities on Gaussian distribution attract many attentions,in which a famous example is the Gaussian minimum conjecture,which says that if n ≥2,and (Xi,1 ≤i≤n)is a centered Gaussian random vector,then the inequality E(min1≤i≤n | Xi |) ≥E(min1≤i≤n | Yi |) holds,where Y1,…,Yn are independent centered Gaussian random variables with E(X2i) =E(Y2i) for any i=1,…,n.In this note,we show that this conjecture holds if and only if n=2.关键词
高斯最小值猜测/高斯随机向量Key words
Gaussian minimum conjecture/Gaussian random vector分类
数理科学引用本文复制引用
钟扬帆,马婷,胡泽春..关于高斯最小值猜测的一个注记[J].四川大学学报（自然科学版）,2021,58(6):15-21,7.基金项目
国家自然科学基金(11771309) （11771309）
