An Introduction to Random Matrices

In this course, we will prove some key results in random  matrix  theory (Wigner’s semicircle law, fluctuations around  semicircle, convergence to sine kernel for GUE, BBP phase transition, norm of random  matrices). On our way, we will review various  methods  which have been used in the field (method  of moments,  concentration inequalities,  resolvent identities, Stein’s method,  determinantal processes).