Average Density of States for Hermitian Wigner Matrices

Details Average Density of States for Hermitian Wigner Matrices Average Density of States for Hermitian Wigner Matrices

2010-11-25

arxiv.org/abs/1011.5594v2

Physics

Mathematical Physics

31 pages. Improved conditions

Scientific paper

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 {\it arbitrarily} small intervals converges to the semicircle law, as $N$ tends to infinity.

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