高斯矩阵测度集中不等式的相关证明  

Proof of Concentration Inequality for Gaussian Matrix

作　　者：郑珂 宋儒瑛[1] ZHENG Ke;SONG Ruying(Department of Mathematics,Taiyuan Normal University,Jinzhong 030619,China)

机构地区：[1]太原师范学院数学系,山西晋中030619

出　　处：《太原师范学院学报（自然科学版）》2021年第4期32-36,共5页Journal of Taiyuan Normal University:Natural Science Edition

基　　金：山西省应用基础研究计划项目(201901D211423);山西省高等学校科技创新项目(2019L0783).

摘　　要：Simon Foucart和Holger Rauhut在他们的著作中证明了高斯随机矩阵奇异值的测度集中不等式,相应的复高斯随机矩阵奇异值和亚高斯随机矩阵奇异值是否有类似的测度集中不等式也是值得思考的.著作中还给出了高斯随机矩阵测度集中不等式的一个修正定理但未给出证明.本文通过证明得出了这两个测度集中不等式,并且补充了高斯随机矩阵测度集中不等式修正定理的证明.In their works,Simon fouhart and Holger rauhut proved the measure concentration inequality of singular values of Gaussian random matrices.It is also worth considering whether the corresponding complex Gaussian random matrix singular values and Sub Gaussian random matrix singular values have similar measure concentration inequalities.A modified theorem of inequality in measure set of Gaussian random matrix is also given,but it is not proved.In this paper,the two measure set inequalities are obtained by proof,and the proof of the correction theorem of measure set inequality of Gaussian random matrix is supplemented.

关 键 词：高斯随机矩阵 亚高斯随机矩阵 奇异值 随机向量 测度集中不等式 

分 类 号：O211.5[理学—概率论与数理统计]