题目：Largest Eigenvalues of Principal Minors of Deformed Gaussian Orthogonal Ensembles and Wishart Matrices.
内容简介：Consider a high-dimensional Wishart matrix W= XTX where the entries of X are i.i.d. random variables with mean zero, variance one, and a finite fourth moment η. Motivated by problems in signal processing and high-dimensional statistics, we study the maximum of the largest eigenvalues of any two-by-two principal minors of W. Under certain restrictions on the sample size and the population dimension ofW, we obtain the limiting distribution of the maximum, which follows the Gumbel distribution when η is between 0 and 3, and a new distribution when η exceeds 3. To derive this result, we first address a simpler problem on a new object named a deformed Gaussian orthogonal ensemble (GOE). The Wishart case is then resolved using results from the deformed GOE and a high-dimensional central limit theorem. Our proof strategy combines the Stein-Poisson approximation method, conditioning, U-statistics, and the Hajek projection. This method may also be applicable to other extreme-value problems. Some open questions are posed.
报告人：祁永成
报告人简介：美国Minnesota大学Duluth分校数学与统计系教授, 1987年获得北京大学理学士学位, 1992年获得北京大学概率统计博士学位, 1994年至1997年任教于北京大学概率统计系, 2001年获得美国 Georgia大学统计学博士学位. 祁永成博士的研究方向包括: 概率统计中的极限定理, 极值统计, 经验似然方法, 高维数据与随机矩阵理论等. 若干研究成果发表在Annals of Statistics, Transactions of the American Mathematical Society, Journal of Theoretical Probability, Statistica Sinica, Scandinavian Journal of Statistics, Journal of Multivariate Analysis, Journal of Mathematical Physics, Insurance: Mathematics and Economics, Stochastic Processes and their Applications, Journal of Applied Probability等专业杂志上. 目前已经发表论文110余篇.
时 间：2025年7月31日（周四）下午16：00开始
地 点：石牌校区南海楼338数学系师生研讨室
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