Hitting probability of Gaussian random fields and collision of eigenvalues of random matrices
报告题目(Title)：Hitting probability of Gaussian random fields and collision of eigenvalues of random matrices
报告人(Speaker)：宋健 教授 (山东大学)
地点(Place)：后主楼 1220
时间(Time)：2021年10月15日 (周五) 下午4:00-5:00
邀请人(Inviter)：何辉
报告摘要
Let $X =\{X(t), t\in R^N\}$ be a centered Gaussian random field with values in $R^d$ and let $F\in R^d\setminus\{0\}$ be a Borel set. We provide a sufficient condition for $F$ to be polar for $X$, i.e., $P(X(t) \in F \text{ for some }t\in R^N) = 0.$ By applying this condition, we solve a problem on the existence of collisions of the eigenvalues of random matrices with Gaussian random field entries in critical dimension that was left open in [Jaramillo-Nualart (2020)] and [Song-Xiao-Yuan (2021)]. This talk is based on joint works with Cheuk-Yin Lee, Yimin Xiao, and Wangjun Yuan.
