Average Density of States for Hermitian Wigner Matrices

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.

31 pages. Improved conditions

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Cited by in corpus (3)

• Random matrices: The Four Moment Theorem for Wigner ensembles
• Random matrices: Universal properties of eigenvectors
• The Wigner-Dyson-Mehta bulk universality conjecture for Wigner matrices