In this paper, we survey some recent progress on rigorously establishing the
universality of various spectral statistics of Wigner Hermitian random matrix
ensembles, focusing on the Four Moment Theorem and its refinements and
applications, including the universality of the sine kernel and the Central
limit theorem of several spectral parameters.
We also take the opportunity here to issue some errata for some of our
previous papers in this area.Comment: 58 page