Universality of generalized Wigner matrices
Horng‐Tzer Yau · Oxford University Press eBooks · 2012
This chapter reviews recent progress on the universality of eigenvalue distributions of generalized Wigner matrices in the bulk and at the edges. It discusses first the local semicircle law, which underlies many of the results. Universality for Gaussian divisible ensembles is then established via the local relaxation flow. Finally, the results are extended to general ensembles by Green's function comparison theorem.