Target Audience：Graduate students
This course will give a brief introduction to random matrix theory. Some topics we plan to cover are: Wigner semicircle law, the moment method, the resolvent method, invariant ensembles, Wigner matrices, sample covariance matrices, bulk universality, edge universality, rigidity of eigenvalues, Dyson Brownian motion, Tracy-Widom law, and free probability.
Probability, Stochastic Processes
(1) A Dynamical Approach to Random Matrix, by László Erdös and Horng-Tzer Yau.
(2) Topics in random matrix theory, by Terence Tao.
Dr. Fan Yang(M) is an associate Professor at Yau Mathematical Sciences Center. Prior to joining YMSC, he was a postdoctoral researcher with the Department of Statistics and Data Science at the University of Pennsylvania from 2019 to 2022. He received the Ph.D. degree in mathematics from the University of California, Los Angeles in 2019, the Ph.D. degree in physics from the Chinese University of Hong Kong in 2014, and the Bachelor's degree from Tsinghua University in 2009. His research interests include probability and statistics, with a focus on random matrix theory and its applications to mathematical physics, high-dimensional statistics, and machine learning.