報(bào)告人：李一霆 教授

報(bào)告題目：Central limit theorem for the linear spectral statistics of sample covariance matrix with random population

報(bào)告時(shí)間：2025年11月28日（周五）上午9：00

報(bào)告地點(diǎn)：云龍校區(qū)2號(hào)樓224教室

主辦單位：數(shù)學(xué)與統(tǒng)計(jì)學(xué)院、數(shù)學(xué)研究院、科學(xué)技術(shù)研究院

報(bào)告人簡(jiǎn)介：

李一霆，本科和碩士畢業(yè)于北京大學(xué)，博士畢業(yè)于布蘭戴斯大學(xué)。曾在瑞典皇家理工學(xué)院、法國(guó)國(guó)家科學(xué)研究中心、韓國(guó)科學(xué)技術(shù)院從事科研工作，現(xiàn)為湖南大學(xué)教授。研究方向?yàn)楦怕收?，特別是隨機(jī)矩陣?yán)碚摗?/p>

報(bào)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.