Please use this identifier to cite or link to this item: doi:10.22028/D291-30661
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Title: Applications of realizations (aka linearizations) to free probability
Author(s): Helton, J. William
Mai, Tobias
Speicher, Roland
Language: English
Title: Journal of functional analysis
Volume: 274
Issue: 1
Startpage: 1
Endpage: 79
Publisher/Platform: Elsevier
Year of Publication: 2018
Publikation type: Journal Article
Abstract: We show how the combination of new “linearization” ideas in free probability theory with the powerful “realization” machinery – developed over the last 50 years in fields including systems engineering and automata theory – allows solving the problem of determining the eigenvalue distribution (or even the Brown measure, in the non-selfadjoint case) of noncommutative rational functions of random matrices when their size tends to infinity. Along the way we extend evaluations of noncommutative rational expressions from matrices to stably finite algebras, e.g. type II1 von Neumann algebras, with a precise control of the domains of the rational expressions. The paper provides sufficient background information, with the intention that it should be accessible both to functional analysts and to algebraists.
DOI of the first publication: 10.1016/j.jfa.2017.10.003
URL of the first publication: https://www.sciencedirect.com/science/article/pii/S0022123617303798
Link to this record: hdl:20.500.11880/28960
http://dx.doi.org/10.22028/D291-30661
ISSN: 0022-1236
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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