Local elliptic law

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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.

Original languageEnglish
JournalBernoulli
Volume28
Issue number2
Pages (from-to)886-909
ISSN1350-7265
DOIs
Publication statusPublished - May 2022

Bibliographical note

Publisher Copyright:
© 2022 ISI/BS.

    Research areas

  • Eigenvector delocalisation, Elliptic ensemble, Local law, Matrix Dyson equation

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