Description:

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.

Prerequisite：

Probability, Stochastic Processes

Reference：

(1) A Dynamical Approach to Random Matrix, by László Erdös and Horng-Tzer Yau.

(2) Topics in random matrix theory, by Terence Tao.