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arXiv · 1011.5594

Average Density of States for Hermitian Wigner Matrices

Anna Maltsev·Benjamin Schlein
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Abstract

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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Anna Maltsev, Benjamin Schlein. 2011-03-13. Average Density of States for Hermitian Wigner Matrices. https://arxiv.org/abs/1011.5594

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