报告题目：Asymptotic Analysis for Extreme Eigenvalues of Principal Minors of Random Matrices

主 讲 人： 姜铁锋 教授

报告时间： 2025年11月28日周五下午13:30-15:30

报告地点： 数理楼224

报告摘要： Consider a high-dimensional Wishart matrix W =X' X 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 of W, 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.

个人简介：姜铁锋，美国斯坦福大学博士毕业，美国明尼苏达大学统计系终身教授，美国NSF Career Award获得者，现为香港中文大学深圳分校数据科学学院教授。主要从事概率统计及其相关领域的研究工作，特别是在概率论、高维统计以及纯数学等交叉学科取得了突破性的进展。姜教授解决的“哈尔西矩阵被独立随机变量逼近”的结果被用于量子计算的研究中。姜教授目前已发表论文50多篇，其中绝大部分发表在国际顶尖的概率统计与机器学习杂志上，包括《Ann. Probab.》、《Probab. Theor. Rel. Fields》、《Ann. Stat.》、《Ann. Appl. Probab.》、《J. Mach. Learn Res.》、《J. Number Theory》及《Transactions of American Mathematical Society》等。