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We consider $N\times N$ Hermitian Wigner random matrices $H$ where the probability density for each matrix element is given by the density $\nu(x)= e^{- U(x)}$.
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Erdős, L., Schlein, B., Yau, H.-T.: Semicircle law on short scales and delocalization of eigenvectors for Wigner random matrices. Accepted in Ann. Probab. Preprint. arXiv.org:0711.1730
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