Time: 19:00-21:00, every Thursday, from November 15th, 2018 to January 10th, 2019 

In this short course, we will introduce some basic concepts in the random matrix theory, including:
1) Wigner’s universality theorem for Wigner’s matrices.
2) Large deviation principle for empirical measures of eigenvalues of invariant ensemble (GUE, GOE, GSE).
3) Gap probabilities for GUE.
4) Stochastic analysis for random matrices: Dyson Brownian motion.
5) Tridiagonal matrix models and the beta-ensembles.

References:
1) An introduction to random matrices, by G. Anderson, A. Guionnet, O. Zeitouni
2) Topics in Random Matrix Theory, by Terence Tao
3) random Matrix Theory: Invariant Ensembles and Universality, by P. Deift, D. Gioev