随机矩阵概率不等式类的证明  

The Proof of Probability Inequality of Random Matrix

作　　者：郑珂 宋儒瑛[1] 

机构地区：[1]太原师范学院数学系,山西 晋中

出　　处：《应用数学进展》2021年第7期2410-2418,共9页Advances in Applied Mathematics

摘　　要：在证明随机矩阵满足限制等距性质以及估计限制等距常数时,Khintchine不等式、Hoeffding型不等式以及Bernstein型不等式都发挥着重要的作用。在实际应用当中,这三种不等式根据随机变量类别的不同又有很多变化。本文重点补充证明了当随机变量为矩阵时的Khintchine不等式、Hoeffding型不等式以及Bernstein型不等式,这些不等式在随机测量矩阵稀疏恢复证明过程中起到关键作用。Khintchine’s inequality, Hoeffding’s inequality and Bernstein’s inequality play an important role in proving that random matrix satisfies the property of restricted isometry and estimating the constant of restricted isometry. In practical application, these three inequalities have many changes according to the different types of random variables. In this paper, we mainly prove the Khintchine inequality, Hoeffding type inequality and Bernstein type inequality when the random variable is a matrix. These inequalities play a key role in the proof of sparse restoration of random measurement matrix.

关 键 词：限制等距性质 亚高斯随机变量 标准高斯随机变量 Khintchine不等式 Hoeffding型不等式 BERNSTEIN型不等式 

分 类 号：G63[文化科学—教育学]