Spherical functions approach to sums of Random Hermitian Matrices

Autores
Kuijlaars, Arno B. J.; Román, Pablo Manuel
Año de publicación
2017
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
We present an approach to sums of random Hermitian matrices via the theory of spher- ical functions for the Gelfand pair (U(n) Herm(n), U(n)). It is inspired by a similar approach of Kieburg and Kösters for products of random matrices. The spherical func- tions have determinantal expressions because of the Harish-Chandra/Itzykson?Zuber integral formula. It leads to remarkably simple expressions for the spherical transform and its inverse. The spherical transform is applied to sums of unitarily invariant ran- dom matrices from polynomial ensembles and the subclass of polynomial ensembles of derivative type (in the additive sense), which turns out to be closed under addition. We finally present additional detailed calculations for the sum with a random matrix from a Laguerre unitary ensemble.
Fil: Kuijlaars, Arno B. J.. Katholikie Universiteit Leuven; Bélgica
Fil: Román, Pablo Manuel. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Centro de Investigación y Estudios de Matemática. Universidad Nacional de Córdoba. Centro de Investigación y Estudios de Matemática; Argentina
Materia
SPHERICAL FUNCTIONS
RANDOM MATRICES
SUMS OF RANDOM MATRICES
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/60242
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/60242
network_acronym_str CONICETDig
repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling Spherical functions approach to sums of Random Hermitian MatricesKuijlaars, Arno B. J.Román, Pablo ManuelSPHERICAL FUNCTIONSRANDOM MATRICESSUMS OF RANDOM MATRICEShttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1We present an approach to sums of random Hermitian matrices via the theory of spher- ical functions for the Gelfand pair (U(n) Herm(n), U(n)). It is inspired by a similar approach of Kieburg and Kösters for products of random matrices. The spherical func- tions have determinantal expressions because of the Harish-Chandra/Itzykson?Zuber integral formula. It leads to remarkably simple expressions for the spherical transform and its inverse. The spherical transform is applied to sums of unitarily invariant ran- dom matrices from polynomial ensembles and the subclass of polynomial ensembles of derivative type (in the additive sense), which turns out to be closed under addition. We finally present additional detailed calculations for the sum with a random matrix from a Laguerre unitary ensemble.Fil: Kuijlaars, Arno B. J.. Katholikie Universiteit Leuven; BélgicaFil: Román, Pablo Manuel. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Centro de Investigación y Estudios de Matemática. Universidad Nacional de Córdoba. Centro de Investigación y Estudios de Matemática; ArgentinaOxford University Press2017-07info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/60242Kuijlaars, Arno B. J.; Román, Pablo Manuel; Spherical functions approach to sums of Random Hermitian Matrices; Oxford University Press; International Mathematics Research Notices; 7-20171073-79281687-0247CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/https://academic.oup.com/imrn/article-lookup/doi/10.1093/imrn/rnx146info:eu-repo/semantics/altIdentifier/doi/10.1093/imrn/rnx146info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-29T10:30:19Zoai:ri.conicet.gov.ar:11336/60242instacron:CONICETInstitucionalhttp://ri.conicet.gov.ar/Organismo científico-tecnológicoNo correspondehttp://ri.conicet.gov.ar/oai/requestdasensio@conicet.gov.ar; lcarlino@conicet.gov.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:34982025-09-29 10:30:20.041CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Spherical functions approach to sums of Random Hermitian Matrices
title Spherical functions approach to sums of Random Hermitian Matrices
spellingShingle Spherical functions approach to sums of Random Hermitian Matrices
Kuijlaars, Arno B. J.
SPHERICAL FUNCTIONS
RANDOM MATRICES
SUMS OF RANDOM MATRICES
title_short Spherical functions approach to sums of Random Hermitian Matrices
title_full Spherical functions approach to sums of Random Hermitian Matrices
title_fullStr Spherical functions approach to sums of Random Hermitian Matrices
title_full_unstemmed Spherical functions approach to sums of Random Hermitian Matrices
title_sort Spherical functions approach to sums of Random Hermitian Matrices
dc.creator.none.fl_str_mv Kuijlaars, Arno B. J.
Román, Pablo Manuel
author Kuijlaars, Arno B. J.
author_facet Kuijlaars, Arno B. J.
Román, Pablo Manuel
author_role author
author2 Román, Pablo Manuel
author2_role author
dc.subject.none.fl_str_mv SPHERICAL FUNCTIONS
RANDOM MATRICES
SUMS OF RANDOM MATRICES
topic SPHERICAL FUNCTIONS
RANDOM MATRICES
SUMS OF RANDOM MATRICES
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv We present an approach to sums of random Hermitian matrices via the theory of spher- ical functions for the Gelfand pair (U(n) Herm(n), U(n)). It is inspired by a similar approach of Kieburg and Kösters for products of random matrices. The spherical func- tions have determinantal expressions because of the Harish-Chandra/Itzykson?Zuber integral formula. It leads to remarkably simple expressions for the spherical transform and its inverse. The spherical transform is applied to sums of unitarily invariant ran- dom matrices from polynomial ensembles and the subclass of polynomial ensembles of derivative type (in the additive sense), which turns out to be closed under addition. We finally present additional detailed calculations for the sum with a random matrix from a Laguerre unitary ensemble.
Fil: Kuijlaars, Arno B. J.. Katholikie Universiteit Leuven; Bélgica
Fil: Román, Pablo Manuel. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Centro de Investigación y Estudios de Matemática. Universidad Nacional de Córdoba. Centro de Investigación y Estudios de Matemática; Argentina
description We present an approach to sums of random Hermitian matrices via the theory of spher- ical functions for the Gelfand pair (U(n) Herm(n), U(n)). It is inspired by a similar approach of Kieburg and Kösters for products of random matrices. The spherical func- tions have determinantal expressions because of the Harish-Chandra/Itzykson?Zuber integral formula. It leads to remarkably simple expressions for the spherical transform and its inverse. The spherical transform is applied to sums of unitarily invariant ran- dom matrices from polynomial ensembles and the subclass of polynomial ensembles of derivative type (in the additive sense), which turns out to be closed under addition. We finally present additional detailed calculations for the sum with a random matrix from a Laguerre unitary ensemble.
publishDate 2017
dc.date.none.fl_str_mv 2017-07
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
http://purl.org/coar/resource_type/c_6501
info:ar-repo/semantics/articulo
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/11336/60242
Kuijlaars, Arno B. J.; Román, Pablo Manuel; Spherical functions approach to sums of Random Hermitian Matrices; Oxford University Press; International Mathematics Research Notices; 7-2017
1073-7928
1687-0247
CONICET Digital
CONICET
url http://hdl.handle.net/11336/60242
identifier_str_mv Kuijlaars, Arno B. J.; Román, Pablo Manuel; Spherical functions approach to sums of Random Hermitian Matrices; Oxford University Press; International Mathematics Research Notices; 7-2017
1073-7928
1687-0247
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/url/https://academic.oup.com/imrn/article-lookup/doi/10.1093/imrn/rnx146
info:eu-repo/semantics/altIdentifier/doi/10.1093/imrn/rnx146
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
dc.publisher.none.fl_str_mv Oxford University Press
publisher.none.fl_str_mv Oxford University Press
dc.source.none.fl_str_mv reponame:CONICET Digital (CONICET)
instname:Consejo Nacional de Investigaciones Científicas y Técnicas
reponame_str CONICET Digital (CONICET)
collection CONICET Digital (CONICET)
instname_str Consejo Nacional de Investigaciones Científicas y Técnicas
repository.name.fl_str_mv CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicas
repository.mail.fl_str_mv dasensio@conicet.gov.ar; lcarlino@conicet.gov.ar
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score 13.070432

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