Title: Spectral and eigenvector statistics of random matrices

Abstract:

I review recent results on the spectral and eigenvector statistics of
large random matrices. In particular, I cover the bulk and edge
universalities of generalized Wigner matrices. I also outline the
universality of eigenvectors associated with eigenvalues near the
spectral edge. In addition to generalized Wigner matrices, I consider
the Erd?s-R?nyi graph, and discuss its spectral universality as well
as the complete delocalization of its eigenvectors. Finally, I sketch
the main ingredients of the proofs. (Joint work with L. Erd?s, H.T.
Yau and J. Yin.)