Local elliptic law
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Local elliptic law. / Alt, Johannes; Krüger, Torben.
I: Bernoulli, Bind 28, Nr. 2, 05.2022, s. 886-909.Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt
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TY - JOUR
T1 - Local elliptic law
AU - Alt, Johannes
AU - Krüger, Torben
N1 - Publisher Copyright: © 2022 ISI/BS.
PY - 2022/5
Y1 - 2022/5
N2 - 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.
AB - 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.
KW - Eigenvector delocalisation
KW - Elliptic ensemble
KW - Local law
KW - Matrix Dyson equation
UR - http://www.scopus.com/inward/record.url?scp=85128902508&partnerID=8YFLogxK
U2 - 10.3150/21-BEJ1370
DO - 10.3150/21-BEJ1370
M3 - Journal article
AN - SCOPUS:85128902508
VL - 28
SP - 886
EP - 909
JO - Bernoulli
JF - Bernoulli
SN - 1350-7265
IS - 2
ER -
ID: 308490176