Hitting probability of Gaussian random fields and collision of
eigenvalues of random matrices
袁望钧 博士
Host： 段金桥教授
Date： 2023年7月25日 (周二)
Time： 16:00-17:00 P.M.
Venue： Tencent Meeting ID：812-622-494
国际创新创业社区A5栋1806会议室
Abstract：
Let $X = \{ X(t),t \in R^N\}$ be a centered Gaussian random field with values in $R^d$ satisfying certain conditions and let $F \subset R^d$ be a Borel set. In the talk, we provide a sufficient condition for $F$ to be polar for $X$, i.e. $P(X(t) \in F$ for some $t \in R^N$) = 0, which improves significantly the existence results. We provide a variety of examples of Gaussian random field for which our result is applicable. Moreover, we solve a problem on the existence of collisions of the eigenvalues of random matrices with Gaussian random field entries that was left open in Jaramillo and Nualart [Random Matrices Theory Appl. 9 (2020), p. 26] and Song et al. [J. Math. Anal. Appl. 502 (2021), p. 22].
Biography：
Wangjun Yuan is a postdoc researcher at the University of Luxembourg working with Mark Podolskij. Before joining University of Luxembourg, he has been a postdoc fellow at University of Ottawa supported by Raluca Balan from 2021 to 2022. He got a bachelor's degree in mathematics from University of Science and Technology of China in 2017, and then a Ph.D. degree in mathematics from The University of Hong Kong in 2021 under the supervision of Jian Song, Guangyue Han and Jianfeng Yao.
His research interests are mainly in the field of random matrix theory, stochastic differential equation, stochastic partially differential equation and Malliavin calculus.
