報告人：李一霆 教授

報告題目：Central limit theorem for the linear spectral statistics of sample covariance matrix with random population

報告時間：2025年11月28日（周五）上午9：00

報告地點：云龍校區2號樓224教室

主辦單位：數學與統計學院、數學研究院、科學技術研究院

報告人簡介：

李一霆，本科和碩士畢業于北京大學，博士畢業于布蘭戴斯大學。曾在瑞典皇家理工學院、法國國家科學研究中心、韓國科學技術院從事科研工作，現為湖南大學教授。研究方向為概率論，特別是隨機矩陣理論。

報告摘要：

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.