单位球的高斯测度与高斯相关不等式

上海大学学报(自然科学版) ›› 2009, Vol. 15 ›› Issue (4): 375-379.

单位球的高斯测度与高斯相关不等式

肖小溅何斌吾

上海大学理学院，上海 200444

收稿日期:2008-03-09 出版日期:2009-08-30 发布日期:2009-08-30
通讯作者: 何斌吾(1957～)，男，教授，博士生导师，博士，研究方向为凸几何、几何分析. E-mail:hebinwu@shu.edu.cn
基金资助:
国家自然科学基金资助项目（10671119）

Gaussian Measure of Unit Ball and Gaussian Correlation Inequality

College of Sciences, Shanghai University, Shanghai 200444, China

Received:2008-03-09 Online:2009-08-30 Published:2009-08-30

摘要/Abstract

摘要：

利用n维欧氏单位球的高斯测度,证明在n维欧氏空间中,如果2个凸体是正交的双锥椭球,那么高斯相关不等式成立;若2个双锥椭球作适当的旋转后交为球，则相关不等式也成立.

关键词: 凸体;高斯测度;相关不等式

Abstract:

Using the Gaussian measure of the n dimensional Euclidean unit ball, it is shown that the Gaussian correlation inequality is true for two orthogonal double cones ellipsoids. Furthermore, the Gaussian correlation inequality is also true for two double cones ellipsoids if the intersection of their images under rotation transformation is ball.

Key words: convex body; Gaussian measure; correlation inequality

中图分类号:

O186.5

肖小溅何斌吾. 单位球的高斯测度与高斯相关不等式[J]. 上海大学学报(自然科学版), 2009, 15(4): 375-379.

XIAO Xiao-Jian, HE Bin-Wu. Gaussian Measure of Unit Ball and Gaussian Correlation Inequality[J]. Journal of Shanghai University（Natural Science Edition）, 2009, 15(4): 375-379.