Hitting probabilities of Gaussian random fields and collision of eigenvalues of random matrices
李卓彥教授國立清華大學數學系 15:30 – 17:00 鴻經館 M107
Abstract：
In this talk, I will discuss hitting probabilities of d-dimensional stochastic processes and random fields. I will start by reviewing some existing results on probability bounds for a process to hit a given set. Those results determine the critical dimension above which the set is polar (i.e., the set will not be hit almost surely), but in general do not determine whether the set is polar in the critical dimension. I will present a new sufficient condition for a compact set to be polar for a class of Gaussian random fields including fractional Brownian fields and systems of stochastic PDEs. Our result also solves an open problem on the collisions of eigenvalues of random matrices with Gaussian random field entries. This is joint work with Jian Song, Yimin Xiao and Wangjun Yuan.