Average Density of States of Wigner Matrices
Talk by Prof. Dr. Benjamin Schlein
Date: 04.03.11 Time: 10.45 - 11.45 Room: ETH HIT E 41.1
Abstract: the entries of an NxN Wigner matrices are (up to symmetry constraints) independent and identically distributed random variables. In the limit of large N, the density of states on intervals containing a large number of eigenvalues converges to the semicircle law with probability one. On smaller intervals, the density of states fluctuates and convergence in probability cannot hold true. It turns out, however, that the average density of states converges to the semicircle law on arbitrarily small intervals.