次高斯复随机矩阵的算子范数估计  

The operator norm estimation of sub-Gaussian complex random matrix

作　　者：范俊辉 庄智涛 FAN Junhui;ZHUANG Zhitao(School of Mathematics and Statistics,North China University of Water Resources and Electric Power,Zhengzhou 450046,China)

机构地区：[1]华北水利水电大学数学与统计学院,河南郑州450046

出　　处：《河南工程学院学报（自然科学版）》2023年第4期71-78,共8页Journal of Henan University of Engineering：Natural Science Edition

摘　　要：在傅里叶光学、量子力学等物理领域,研究对象可用复随机矩阵描述,而复随机矩阵的算子范数估计是研究这些物理问题的重要工具,故对次高斯复随机矩阵的算子范数估计进行了研究。首先将实随机变量的性质推广到复随机变量上,并在此基础上证明了复随机变量的Hoeffding不等式和Bernstein不等式,然后利用ε-网技术给出了次高斯复随机矩阵算子范数的一个双侧界估计,最后用次高斯复随机矩阵范数估计的数值模拟实验验证了结论的准确性。In the field of physics,such as Fourier optics and quantum mechanics,the research object can be described by complex random matrix.And the operator norm estimation of random matrix is an important tool to study these physical problems.In this paper,we study the operator norm estimates of sub-gaussian complex random matrices.Firstly,the properties of real random variables are generalized to complex random variables,and on the basis of that,the Hoeffding′s inequality and Bernstein′s inequality of complex random variables are proved.Secondly,by using-net technique,a two-sided bound estimate of the operator norm of sub-gaussian complex random matrices is given.Finally,numerical experiments are given to verify the conclusion.

关 键 词：次高斯复随机矩阵 ε-网 算子范数估计 

分 类 号：O213[理学—概率论与数理统计]