On the high-density expansion for Euclidean random matrices

Autores
Grigera, Tomás Sebastián; Martin-Mayor, Victor; Parisi, Giorgio; Urbani, Pierfrancesco; Verrocchio, Paolo
Año de publicación
2011
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
Diagrammatic techniques to compute perturbatively the spectral properties of Euclidean random matrices (ERM) in the high-density regime are introduced and discussed in detail. Such techniques are developed in two alternative and very different formulations of the mathematical problem and are shown to give identical results up to second order in the perturbative expansion. One method, based on writing the so-called resolvent function as a Taylor series, allows us to group the diagrams into a small number of topological classes, providing a simple way to determine the infrared (small momenta) behaviour of the theory up to third order, which is of interest for the comparison with experiments. The other method, which reformulates the problem as a field theory, can instead be used to study the infrared behaviour at any perturbative order.
Facultad de Ciencias Exactas
Instituto de Investigaciones Fisicoquímicas Teóricas y Aplicadas
Materia
Ciencias Exactas
Física
random matrix theory and extensions
Nivel de accesibilidad
acceso abierto
Condiciones de uso
http://creativecommons.org/licenses/by-nc-sa/4.0/
Repositorio
SEDICI (UNLP)
Institución
Universidad Nacional de La Plata
OAI Identificador
oai:sedici.unlp.edu.ar:10915/132236
Acceder
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network_name_str SEDICI (UNLP)
spelling On the high-density expansion for Euclidean random matricesGrigera, Tomás SebastiánMartin-Mayor, VictorParisi, GiorgioUrbani, PierfrancescoVerrocchio, PaoloCiencias ExactasFísicarandom matrix theory and extensionsDiagrammatic techniques to compute perturbatively the spectral properties of Euclidean random matrices (ERM) in the high-density regime are introduced and discussed in detail. Such techniques are developed in two alternative and very different formulations of the mathematical problem and are shown to give identical results up to second order in the perturbative expansion. One method, based on writing the so-called resolvent function as a Taylor series, allows us to group the diagrams into a small number of topological classes, providing a simple way to determine the infrared (small momenta) behaviour of the theory up to third order, which is of interest for the comparison with experiments. The other method, which reformulates the problem as a field theory, can instead be used to study the infrared behaviour at any perturbative order.Facultad de Ciencias ExactasInstituto de Investigaciones Fisicoquímicas Teóricas y Aplicadas2011-02info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionArticulohttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfhttp://sedici.unlp.edu.ar/handle/10915/132236enginfo:eu-repo/semantics/altIdentifier/issn/1742-5468info:eu-repo/semantics/altIdentifier/doi/10.1088/1742-5468/2011/02/p02015info:eu-repo/semantics/openAccesshttp://creativecommons.org/licenses/by-nc-sa/4.0/Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International (CC BY-NC-SA 4.0)reponame:SEDICI (UNLP)instname:Universidad Nacional de La Platainstacron:UNLP2025-10-22T17:12:12Zoai:sedici.unlp.edu.ar:10915/132236Institucionalhttp://sedici.unlp.edu.ar/Universidad públicaNo correspondehttp://sedici.unlp.edu.ar/oai/snrdalira@sedici.unlp.edu.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:13292025-10-22 17:12:12.649SEDICI (UNLP) - Universidad Nacional de La Platafalse
dc.title.none.fl_str_mv On the high-density expansion for Euclidean random matrices
title On the high-density expansion for Euclidean random matrices
spellingShingle On the high-density expansion for Euclidean random matrices
Grigera, Tomás Sebastián
Ciencias Exactas
Física
random matrix theory and extensions
title_short On the high-density expansion for Euclidean random matrices
title_full On the high-density expansion for Euclidean random matrices
title_fullStr On the high-density expansion for Euclidean random matrices
title_full_unstemmed On the high-density expansion for Euclidean random matrices
title_sort On the high-density expansion for Euclidean random matrices
dc.creator.none.fl_str_mv Grigera, Tomás Sebastián
Martin-Mayor, Victor
Parisi, Giorgio
Urbani, Pierfrancesco
Verrocchio, Paolo
author Grigera, Tomás Sebastián
author_facet Grigera, Tomás Sebastián
Martin-Mayor, Victor
Parisi, Giorgio
Urbani, Pierfrancesco
Verrocchio, Paolo
author_role author
author2 Martin-Mayor, Victor
Parisi, Giorgio
Urbani, Pierfrancesco
Verrocchio, Paolo
author2_role author
author
author
author
dc.subject.none.fl_str_mv Ciencias Exactas
Física
random matrix theory and extensions
topic Ciencias Exactas
Física
random matrix theory and extensions
dc.description.none.fl_txt_mv Diagrammatic techniques to compute perturbatively the spectral properties of Euclidean random matrices (ERM) in the high-density regime are introduced and discussed in detail. Such techniques are developed in two alternative and very different formulations of the mathematical problem and are shown to give identical results up to second order in the perturbative expansion. One method, based on writing the so-called resolvent function as a Taylor series, allows us to group the diagrams into a small number of topological classes, providing a simple way to determine the infrared (small momenta) behaviour of the theory up to third order, which is of interest for the comparison with experiments. The other method, which reformulates the problem as a field theory, can instead be used to study the infrared behaviour at any perturbative order.
Facultad de Ciencias Exactas
Instituto de Investigaciones Fisicoquímicas Teóricas y Aplicadas
description Diagrammatic techniques to compute perturbatively the spectral properties of Euclidean random matrices (ERM) in the high-density regime are introduced and discussed in detail. Such techniques are developed in two alternative and very different formulations of the mathematical problem and are shown to give identical results up to second order in the perturbative expansion. One method, based on writing the so-called resolvent function as a Taylor series, allows us to group the diagrams into a small number of topological classes, providing a simple way to determine the infrared (small momenta) behaviour of the theory up to third order, which is of interest for the comparison with experiments. The other method, which reformulates the problem as a field theory, can instead be used to study the infrared behaviour at any perturbative order.
publishDate 2011
dc.date.none.fl_str_mv 2011-02
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
Articulo
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://sedici.unlp.edu.ar/handle/10915/132236
url http://sedici.unlp.edu.ar/handle/10915/132236
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/issn/1742-5468
info:eu-repo/semantics/altIdentifier/doi/10.1088/1742-5468/2011/02/p02015
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
http://creativecommons.org/licenses/by-nc-sa/4.0/
Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International (CC BY-NC-SA 4.0)
eu_rights_str_mv openAccess
rights_invalid_str_mv http://creativecommons.org/licenses/by-nc-sa/4.0/
Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International (CC BY-NC-SA 4.0)
dc.format.none.fl_str_mv application/pdf
dc.source.none.fl_str_mv reponame:SEDICI (UNLP)
instname:Universidad Nacional de La Plata
instacron:UNLP
reponame_str SEDICI (UNLP)
collection SEDICI (UNLP)
instname_str Universidad Nacional de La Plata
instacron_str UNLP
institution UNLP
repository.name.fl_str_mv SEDICI (UNLP) - Universidad Nacional de La Plata
repository.mail.fl_str_mv alira@sedici.unlp.edu.ar
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