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
- Institución
- Universidad Nacional de La Plata
- OAI Identificador
- oai:sedici.unlp.edu.ar:10915/132236
Ver los metadatos del registro completo
id |
SEDICI_1dd1c01a87129ad4e82a895927a37154 |
---|---|
oai_identifier_str |
oai:sedici.unlp.edu.ar:10915/132236 |
network_acronym_str |
SEDICI |
repository_id_str |
1329 |
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:UNLP2025-09-29T11:31:17Zoai: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:13292025-09-29 11:31:17.898SEDICI (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 |
_version_ |
1844616192774373376 |
score |
13.070432 |