Semicircle law on short scales and delocalization of eigenvectors for Wigner random matrices

Abstract

We consider N × N Hermitian random matrices with i.i.d. entries. The matrix is normalized so that the average spacing between consecutive eigenvalues is of order 1/N . We study the connection between eigenvalue statistics on microscopic energy scales η ≪ 1 and (de)localization properties of the eigenvectors. Under suitable assumptions on the distribution of… (More)

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@inproceedings{Erds2008SemicircleLO, title={Semicircle law on short scales and delocalization of eigenvectors for Wigner random matrices}, author={L{\'a}szl{\'o} Erdős and Benjamin Schlein}, year={2008} }