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doi:10.22028/D291-30657
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: | SciDok - Der Wissenschaftsserver der Universität des Saarlandes |
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