Average Density of States for Hermitian Wigner Matrices

Analysis Seminar
Wednesday, June 15, 2011 - 2:00pm
1 hour (actually 50 minutes)
Skiles 05
University of Bonn
We consider ensembles of $N \times N$ Hermitian Wigner matrices, whose entries are (up to the symmetry constraints) independent and identically distributed random variables. Assuming sufficient regularity for the probability density function of the entries, we show that the expectation of the density of states on arbitrarily small intervals converges to the semicircle law, as $N$ tends to infinity.