-
活动&公告
活动&公告
报告题目： Universality Transitions in the Logarithmic Law of Random Determinants Beyond the Fourth Moment
报告时间： 2026-10-23 14:00——2026-10-23 15:00
报告人： 刘松昊
报告地点： 腾讯会议：372-598-401
主办单位： 数据科学与人工智能学院
报告摘要：
The logarithm of the absolute determinant is a classical object in random matrix theory. In this talk, we study its Gaussian fluctuations for random matrices with independent, centered, unit-variance real entries, focusing on how the moment assumptions and convergence rates depend on the choice of centering and scaling. We compare three natural normalizations: classical deterministic centering and scaling, exact-mean centering with classical scaling, and normalization by the exact mean and variance. Under logarithmically weakened fourth-moment conditions, we establish central limit theorems and quantitative Berry-Esseen bounds, with additional uniformly bounded density assumptions for the latter two normalizations. Under a uniform fourth-moment bound, the three normalizations yield the optimal Kolmogorov convergence rates log n^{-1/2} log n^{-1}, and log n^{-3/2}, respectively.
报告人简介：
刘松昊，毕业于香港中文大学统计系，现为大连理工大学数学科学学院副教授。主持国家自然科学青年基金。主要研究方向为：概率极限理论，随机图，相依模型，自正则化理论。在PTRF，AAP，Bernoulli，SPA的期刊发表多篇论文。
