报告人：李一霆 教授
报告题目：Central limit theorem for the linear spectral statistics of sample covariance matrix with random population
报告时间：2025年11月28日（周五）上午9：00
报告地点：云龙校区2号楼224教室
主办单位：数学与统计学院、数学研究院、科学技术研究院
报告人简介：
李一霆，本科和硕士毕业于北京大学，博士毕业于布兰戴斯大学。曾在瑞典皇家理工学院、法国国家科学研究中心、韩国科学技术院从事科研工作，现为湖南大学教授。研究方向为概率论，特别是随机矩阵理论。
报告摘要：
Consider the sample covariance matrix (\Sigma^{1/2})XX^*(\Sigma^{1/2}) where X is an M by N random matrix with independent entries and \Sigma is an M by M positive definite diagonal matrix. Use L(f) to denote the linear spectral statistics of the sample covariance matrix with test function f. It is known that if \Sigma is deterministic, then the fluctuation of L(f) converges in distribution to a Gaussian distribution. We prove that if \Sigma is random and is independent of X, then L(f) multiplied by N^{-1/2} converges in distribution to a Gaussian distribution. This phenomenon implies that the randomness of \Sigma weakens the correlation among the eigenvalues of the sample covariance matrix. This is a joint work with Ji Oon Lee.