### DIMACS - Graduate Student Combinatorics Seminar

Title: Optimal local semi-circle law and delocalization

Speaker: **Ke Wang**, Rutgers University

Date: Wednesday, April 6, 2011 12:10pm

Location: Graduate Student Lounge, 7th Floor, Hill Center, Rutgers University, Busch Campus, Piscataway, NJ

Abstract:
Consider a random n×n Hermitian matrix Mn whose upper triangular entries are iid with mean 0, variance 1 and sub-exponential decay. The famous Wigner's semicircle law characterizes the limiting distribution of the eigenvalues of (1/vn) Mn on any fixed interval I=[a,b], which is known as the global spectral statistics. In this talk, I will discuss the local semicircle law, i.e. for intervals whose size may shrink with n, on an optimal scale. As a consequence, the eigenvector delocalization result is obtained. Joint work with Van H. Vu.

Graduate Student Combinatorics Seminars