Spectral Radius and Empirical Law of Product Ensemble
数学专题报告
报告题目(Title)：Spectral Radius and Empirical Law of Product Ensemble
报告人(Speaker)：姜铁锋教授（The Chinese University of Hong Kong at Shenzhen）
地点(Place)：后主楼1124
时间(Time)：2026年4月9日（周四）10:00-11:00
邀请人(Inviter)：何辉
报告摘要
In this talk we investigate asymptotic properties of the eigenvalues from two n by n random matrices as n goes to infinity. The first one is the product of m i.i.d. (complex) Ginibre ensembles, and the second one is that of truncations of m independent Haar unitary matrices which may have different sizes. For the product of Ginibre ensembles, limiting distributions of the spectral radii are obtained when the limit of m/n exists, and explicit empirical distributions of the eigenvalues are obtained regardless of the speed of m compared to n. For the product of truncations of Haar unitary matrices, limits of the empirical distributions are quite rich, depending on m and sizes of Haarunitary matrices. The main techniques we employ are the independence structure of points following a determinantal point process and some estimations of moments for the sum of functions of the eigenvalues.
主讲人简介
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。
