Advanced topics in random matrices

This book provides three accessible panoramas and syntheses on advanced topics in random matrix theory : (1) local semicircle law for Wigner matrices, and applications to eigenvectors delocalization, rigidity of eigenvalues, and fourth moment theorem ; (2) spectrum of random graphs, recent advances on eigenvalues and eigenvectors, and open problems ; (3) deformed random matrices and free probability, unified understanding of various asymptotic phenomena such as spectral measure description, localization and fluctuations of extremal eigenvalues, eigenvectors behavior.