Please use this identifier to cite or link to this item:
Volltext verfügbar? / Dokumentlieferung
doi:10.22028/D291-30661
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: | SciDok - Der Wissenschaftsserver der Universität des Saarlandes |
Files for this record:
There are no files associated with this item.
Items in SciDok are protected by copyright, with all rights reserved, unless otherwise indicated.