报告人：方笑（香港中文大学）

时间：2025年5月24日，10:00-11:00

地点：海纳苑2幢206室

摘要：In the literature of high-dimensional central limit theorems, there is a gap between results for general limiting correlation matrix $\Sigma$ and the strongly non-degenerate case. For the general case where $\Sigma$ may be degenerate, under certain light-tail conditions, when approximating a normalized sum of $n$ independent random vectors by the Gaussian distribution $N(0,\Sigma)$ in multivariate Kolmogorov distance, the best-known error rate has been $O(n^{-1/4})$, subject to logarithmic factors of the dimension. For the strongly non-degenerate case, that is, when the minimum eigenvalue of $\Sigma$ is bounded away from 0, the error rate can be improved to $O(n^{-1/2})$ up to a $\log n$ factor. In this paper, we show that the $O(n^{-1/2})$ rate up to a $\log n$ factor can still be achieved in the degenerate case, provided that the minimum eigenvalue of the limiting correlation matrix of any three components is bounded away from 0.We prove our main results using Stein's method in conjunction with previously unexplored inequalities for the integral of the first three derivatives of the standard Gaussian density over convex polytopes. These inequalities were previously known only for hyperrectangles. Our proof demonstrates the connection between the three-components condition and the third moment Berry--Esseen bound. This is joint work with Yuta Koike (UTokyo), Song-Hao Liu (Sustech) and Yi-Kun Zhao (CUHK).

报告人简介：方笑，香港中文大学统计系副教授。曾获新加坡国立大学博士学位，研究兴趣包括概率极限理论，斯坦因方法，高维中心极限定理等，目前已发表20余篇SCI论文。

联系人：苏中根（suzhonggen@zju.edu.cn）