Please use this identifier to cite or link to this item: doi:10.22028/D291-30657
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Title: Eigenvalues of non-Hermitian random matrices and Brown measure of non-normal operators: Hermitian reduction and linearization method
Author(s): Belinschi, Serban T.
Śniady, Piotr
Speicher, Roland
Language: English
Title: Linear algebra and its applications
Volume: 537
Startpage: 48
Endpage: 83
Publisher/Platform: Elsevier
Year of Publication: 2018
Publikation type: Journal Article
Abstract: We study the Brown measure of certain non-Hermitian operators arising from Voiculescu's free probability theory. Usually those operators appear as the limit in ⋆-moments of certain ensembles of non-Hermitian random matrices, and the Brown measure gives then a canonical candidate for the limit eigenvalue distribution of the random matrices. A prominent class for our operators is given by polynomials in ⋆-free variables. Other explicit examples include R-diagonal elements and elliptic elements, for which the Brown measure was already known, and a new class of triangular-elliptic elements. Our method for the calculation of the Brown measure is based on a rigorous mathematical treatment of the Hermitian reduction method, as considered in the physical literature, combined with subordination and the linearization trick.
DOI of the first publication: 10.1016/j.laa.2017.09.024
URL of the first publication: https://www.sciencedirect.com/science/article/abs/pii/S002437951730558X
Link to this record: hdl:20.500.11880/28959
http://dx.doi.org/10.22028/D291-30657
ISSN: 0024-3795
Date of registration: 6-Apr-2020
Faculty: MI - Fakultät für Mathematik und Informatik
Department: MI - Mathematik
Professorship: MI - Prof. Dr. Roland Speicher
Collections:UniBib – Die Universitätsbibliographie

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