报告题目: Recent advances on eigenvalues of matrix-valued stochastic processes
时 间：2021年11月03日（星期三）下午15：00
地 点：腾讯会议（ID：705 673 857）
主 办：数学与统计学院
参加对象：统计系老师与学生
报告摘要：Since the introduction of Dyson’s Brownian motion in early 1960s, there have been a lot of developments in the investigation of stochastic processes on the space of Hermitian matrices. Their properties, especially, the properties of their eigenvalues have been studied in great detail. In particular, the limiting behaviours of the eigenvalues are found when the dimension of the matrix space tends to infinity, which connects with random matrix theory. This survey reviews a selection of results on the eigenvalues of stochastic processes from the literature of the past three decades. For most recent variations of such processes, such as matrix-valued processes driven by fractional Brownian motion or Brownian sheet, the eigenvalues of them are also discussed in this survey. In the end, some open problems in the area are also proposed. The talk is based on joint works with Jianfeng Yao and Wangjun Yuan.
报告人简介：宋健教授主要研究领域为随机分析、随机偏微分方程、随机矩阵等。2010年博士毕业于堪萨斯大学，2010-2012年任罗格斯大学访问助理教授，2013-2018年任香港大学助理教授，2018年至今任山东大学数学与交叉科学研究中心教授。