题目:大维自协方差矩阵特征值的极限分布

报告人：姚建峰 教授（香港中文大学（深圳））

时间：2024年4月1日 10:30

地点：西大楼108教室

摘要:In this work, we establish a limiting distribution for eigenvalues of a class of auto-covariance matrices. The same distribution has been foundin the literature for a regularized version of these auto-covariance matrices. The original non-regularized auto-covariance matrices are non invertible, thus introducing supplementary difficulties for the study of their eigenvalues through Girko’s Hermitization scheme. The key result in this paper is a new polynomial lower bound for a specific family of least singular values associated to a rank-defective quadratic function of a random matrix with independent and identically distributed entries. Another innovation from the paper is that the lag of the auto-covariance matrices can grow to infinity with the matrix dimension.

个人简介：姚建峰教授于1990年获得巴黎萨克雷大学博士学位，是香港中文大学（深圳）校长讲座教授，数据科学学院统计学学科负责人。姚教授是IMS会士、伯努利数理统计与概率学会科学书记和执行委员会委员、《Journal of Multivariate Analysis》及 《Random Matrices: Theory and Applications》副主编、曾任《Bernoulli》期刊编委，原香港大学教授、山东大学数学学院特聘教授。