Please use this identifier to cite or link to this item: doi:10.22028/D291-30674
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Title: Squared eigenvalue condition numbers and eigenvector correlations from the single ring theorem
Author(s): Belinschi, Serban
Nowak, Maciej A.
Speicher, Roland
Tarnowski, Wojciech
Language: English
Title: Journal of physics : concerned with the fundamental mathematical and computational methods underpinning physics, the journal is particularly relevant to statistical physics, chaotic and complex systems, classical and quantum mechanics and classical and quantum field theory. A, Mathematical and theoretical
Volume: 50
Issue: 10
Startpage: 1
Endpage: 11
Publisher/Platform: IOP Publishing
Year of Publication: 2017
Publikation type: Journal Article
Abstract: We extend the so-called 'single ring theorem' (Feinberg and Zee 1997 Nucl. Phys. B 504 579), also known as the Haagerup–Larsen theorem (Haagerup and Larsen 2000 J. Funct. Anal. 176 331). We do this by showing that in the limit when the size of the matrix goes to infinity a particular correlator between left and right eigenvectors of the relevant non-hermitian matrix X, being the spectral density weighted by the squared eigenvalue condition number, is given by a simple formula involving only the radial spectral cumulative distribution function of X. We show that this object allows the calculation of the conditional expectation of the squared eigenvalue condition number. We give examples and provide a cross-check of the analytic prediction by the large scale numerics.
DOI of the first publication: 10.1088/1751-8121/aa5451
URL of the first publication:
Link to this record: hdl:20.500.11880/28962
ISSN: 1751-8121
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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