Edge universality for non-Hermitian random matrices

We consider large non-Hermitian real or complex random matrices [Formula: see text] with independent, identically distributed centred entries. We prove that their local eigenvalue statistics near the spectral edge, the unit circle, coincide with those of the Ginibre ensemble, i.e. when the matrix el...

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Autores principales: Cipolloni, Giorgio, Erdős, László, Schröder, Dominik
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Springer Berlin Heidelberg 2020
Materias:
Article
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7906960/
https://www.ncbi.nlm.nih.gov/pubmed/33707804
http://dx.doi.org/10.1007/s00440-020-01003-7
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author Cipolloni, Giorgio
Erdős, László
Schröder, Dominik
author_facet Cipolloni, Giorgio
Erdős, László
Schröder, Dominik
author_sort Cipolloni, Giorgio
collection PubMed
description We consider large non-Hermitian real or complex random matrices [Formula: see text] with independent, identically distributed centred entries. We prove that their local eigenvalue statistics near the spectral edge, the unit circle, coincide with those of the Ginibre ensemble, i.e. when the matrix elements of [Formula: see text] are Gaussian. This result is the non-Hermitian counterpart of the universality of the Tracy–Widom distribution at the spectral edges of the Wigner ensemble.
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spelling pubmed-79069602021-03-09 Edge universality for non-Hermitian random matrices Cipolloni, Giorgio Erdős, László Schröder, Dominik Probab Theory Relat Fields Article We consider large non-Hermitian real or complex random matrices [Formula: see text] with independent, identically distributed centred entries. We prove that their local eigenvalue statistics near the spectral edge, the unit circle, coincide with those of the Ginibre ensemble, i.e. when the matrix elements of [Formula: see text] are Gaussian. This result is the non-Hermitian counterpart of the universality of the Tracy–Widom distribution at the spectral edges of the Wigner ensemble. Springer Berlin Heidelberg 2020-09-25 2021 /pmc/articles/PMC7906960/ /pubmed/33707804 http://dx.doi.org/10.1007/s00440-020-01003-7 Text en © The Author(s) 2020 Open AccessThis article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.
spellingShingle Article
Cipolloni, Giorgio
Erdős, László
Schröder, Dominik
Edge universality for non-Hermitian random matrices
title Edge universality for non-Hermitian random matrices
title_full Edge universality for non-Hermitian random matrices
title_fullStr Edge universality for non-Hermitian random matrices
title_full_unstemmed Edge universality for non-Hermitian random matrices
title_short Edge universality for non-Hermitian random matrices
title_sort edge universality for non-hermitian random matrices
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7906960/
https://www.ncbi.nlm.nih.gov/pubmed/33707804
http://dx.doi.org/10.1007/s00440-020-01003-7
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