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Local elliptic law. (English) Zbl 1489.15047

Summary: The empirical eigenvalue distribution of the elliptic random matrix ensemble tends to the uniform measure on an ellipse in the complex plane as its dimension tends to infinity. We show this convergence on all mesoscopic scales slightly above the typical eigenvalue spacing in the bulk spectrum with an optimal convergence rate. As a corollary we obtain complete delocalisation for the corresponding eigenvectors in any basis.

MSC:

15B52 Random matrices (algebraic aspects)
15A18 Eigenvalues, singular values, and eigenvectors
60B20 Random matrices (probabilistic aspects)
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