报告人：刘竣文 博士
报告题目：Edgeworth expansions of extreme eigenvalue distributions for random unitary ensembles
报告时间：2026年6月23日（周二）下午3：00
报告地点：云龙校区6号楼318会议室
主办单位：数学与统计学院、数学研究院、科学技术研究院
报告人简介：
刘竣文，复旦大学博士五年级研究生，师从张仑教授。主要研究方向为随机矩阵理论及其与可积系统的联系。目前已有两篇论文分别发表于Journal of the London Mathematical Society和Nonlinearity。
报告摘要：
This talk discusses Edgeworth-type expansions for eigenvalue statistics at the spectral edges of unitary random matrix ensembles. Classical edge limits are described by the Airy and Bessel kernels, leading to Tracy-Widom and hard-edge gap distributions. We study how these limiting laws are refined by finite-size correction terms for general varying-weight ensembles. The results provide higher-order expansions both for correlation kernels and for the associated largest- and smallest-eigenvalue distributions, extending known formulas from classical Gaussian and Laguerre ensembles to a broader setting.
