CORRELATED RANDOM MATRICES: BAND RIGIDITY AND EDGE UNIVERSALITY

We prove edge universality for a general class of correlated real symmetric or complex Hermitian Wigner matrices with arbitrary expectation. Our theorem also applies to internal edges of the self-consistent density of states. In particular, we establish a strong form of band rigidity which excludes...

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Veröffentlicht in:The Annals of probability 2020-03, Vol.48 (2), p.963-1001
Hauptverfasser: Alt, Johannes, ErdőS, László, Krüger, Torben, Schröder, Dominik
Format: Artikel
Sprache:eng
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Zusammenfassung:We prove edge universality for a general class of correlated real symmetric or complex Hermitian Wigner matrices with arbitrary expectation. Our theorem also applies to internal edges of the self-consistent density of states. In particular, we establish a strong form of band rigidity which excludes mismatches between location and label of eigenvalues close to internal edges in these general models.
ISSN:0091-1798
2168-894X
DOI:10.1214/19-AOP1379