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).