## Local elliptic law

Publikation: Bidrag til tidsskriftTidsskriftartikelForskningfagfællebedømt

#### Standard

Local elliptic law. / Alt, Johannes; Krüger, Torben.

I: Bernoulli, Bind 28, Nr. 2, 05.2022, s. 886-909.

Publikation: Bidrag til tidsskriftTidsskriftartikelForskningfagfællebedømt

#### Harvard

Alt, J & Krüger, T 2022, 'Local elliptic law', Bernoulli, bind 28, nr. 2, s. 886-909. https://doi.org/10.3150/21-BEJ1370

#### APA

Alt, J., & Krüger, T. (2022). Local elliptic law. Bernoulli, 28(2), 886-909. https://doi.org/10.3150/21-BEJ1370

#### Vancouver

Alt J, Krüger T. Local elliptic law. Bernoulli. 2022 maj;28(2):886-909. https://doi.org/10.3150/21-BEJ1370

#### Author

Alt, Johannes ; Krüger, Torben. / Local elliptic law. I: Bernoulli. 2022 ; Bind 28, Nr. 2. s. 886-909.

#### Bibtex

@article{c11f582868e24e9982db1a4cf671cf51,
title = "Local elliptic law",
abstract = "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.",
keywords = "Eigenvector delocalisation, Elliptic ensemble, Local law, Matrix Dyson equation",
author = "Johannes Alt and Torben Kr{\"u}ger",
year = "2022",
month = may,
doi = "10.3150/21-BEJ1370",
language = "English",
volume = "28",
pages = "886--909",
journal = "Bernoulli",
issn = "1350-7265",
publisher = "International Statistical Institute",
number = "2",

}

#### RIS

TY - JOUR

T1 - Local elliptic law

AU - Alt, Johannes

AU - Krüger, Torben

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