Spectral density of dense random networks and the breakdown of the Wigner semicircle law
Autor(a) principal: | |
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Data de Publicação: | 2020 |
Outros Autores: | |
Tipo de documento: | Artigo |
Idioma: | eng |
Título da fonte: | Repositório Institucional da UFRGS |
Texto Completo: | http://hdl.handle.net/10183/218523 |
Resumo: | Although the spectra of random networks have been studied for a long time, the influence of network topology on the dense limit of network spectra remains poorly understood. By considering the configuration model of networks with four distinct degree distributions, we show that the spectral density of the adjacency matrices of dense random networks is determined by the strength of the degree fluctuations. In particular, the eigenvalue distribution of dense networks with an exponential degree distribution is governed by a simple equation, from which we uncover a logarithmic singularity in the spectral density. We also derive a relation between the fourth moment of the eigenvalue distribution and the variance of the degree distribution, which leads to a sufficient condition for the breakdown of the Wigner semicircle law for dense random networks. Based on the same relation, we propose a classification scheme of the distinct universal behaviors of the spectral density in the dense limit. Our theoretical findings should lead to important insights on the mean-field behavior of models defined on graphs. |
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Metz, Fernando LucasSilva, Jeferson Dias da2021-03-10T04:21:07Z20202643-1564http://hdl.handle.net/10183/218523001122370Although the spectra of random networks have been studied for a long time, the influence of network topology on the dense limit of network spectra remains poorly understood. By considering the configuration model of networks with four distinct degree distributions, we show that the spectral density of the adjacency matrices of dense random networks is determined by the strength of the degree fluctuations. In particular, the eigenvalue distribution of dense networks with an exponential degree distribution is governed by a simple equation, from which we uncover a logarithmic singularity in the spectral density. We also derive a relation between the fourth moment of the eigenvalue distribution and the variance of the degree distribution, which leads to a sufficient condition for the breakdown of the Wigner semicircle law for dense random networks. Based on the same relation, we propose a classification scheme of the distinct universal behaviors of the spectral density in the dense limit. Our theoretical findings should lead to important insights on the mean-field behavior of models defined on graphs.application/pdfengPhysical Review Research. College Park. Vol. 2, no. 4 (Oct./Dec. 2020), 043116, 12 p.Lei do semicírculo de WignerSistemas dinâmicosMatrizes aleatóriasSpectral density of dense random networks and the breakdown of the Wigner semicircle lawEstrangeiroinfo:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/openAccessreponame:Repositório Institucional da UFRGSinstname:Universidade Federal do Rio Grande do Sul (UFRGS)instacron:UFRGSTEXT001122370.pdf.txt001122370.pdf.txtExtracted Texttext/plain64335http://www.lume.ufrgs.br/bitstream/10183/218523/2/001122370.pdf.txt01f62aee10a813d1c81fceabc9076883MD52ORIGINAL001122370.pdfTexto completo (inglês)application/pdf694800http://www.lume.ufrgs.br/bitstream/10183/218523/1/001122370.pdf63dbb24a8c537c07af380cad54622db5MD5110183/2185232023-05-21 03:27:28.168959oai:www.lume.ufrgs.br:10183/218523Repositório de PublicaçõesPUBhttps://lume.ufrgs.br/oai/requestopendoar:2023-05-21T06:27:28Repositório Institucional da UFRGS - Universidade Federal do Rio Grande do Sul (UFRGS)false |
dc.title.pt_BR.fl_str_mv |
Spectral density of dense random networks and the breakdown of the Wigner semicircle law |
title |
Spectral density of dense random networks and the breakdown of the Wigner semicircle law |
spellingShingle |
Spectral density of dense random networks and the breakdown of the Wigner semicircle law Metz, Fernando Lucas Lei do semicírculo de Wigner Sistemas dinâmicos Matrizes aleatórias |
title_short |
Spectral density of dense random networks and the breakdown of the Wigner semicircle law |
title_full |
Spectral density of dense random networks and the breakdown of the Wigner semicircle law |
title_fullStr |
Spectral density of dense random networks and the breakdown of the Wigner semicircle law |
title_full_unstemmed |
Spectral density of dense random networks and the breakdown of the Wigner semicircle law |
title_sort |
Spectral density of dense random networks and the breakdown of the Wigner semicircle law |
author |
Metz, Fernando Lucas |
author_facet |
Metz, Fernando Lucas Silva, Jeferson Dias da |
author_role |
author |
author2 |
Silva, Jeferson Dias da |
author2_role |
author |
dc.contributor.author.fl_str_mv |
Metz, Fernando Lucas Silva, Jeferson Dias da |
dc.subject.por.fl_str_mv |
Lei do semicírculo de Wigner Sistemas dinâmicos Matrizes aleatórias |
topic |
Lei do semicírculo de Wigner Sistemas dinâmicos Matrizes aleatórias |
description |
Although the spectra of random networks have been studied for a long time, the influence of network topology on the dense limit of network spectra remains poorly understood. By considering the configuration model of networks with four distinct degree distributions, we show that the spectral density of the adjacency matrices of dense random networks is determined by the strength of the degree fluctuations. In particular, the eigenvalue distribution of dense networks with an exponential degree distribution is governed by a simple equation, from which we uncover a logarithmic singularity in the spectral density. We also derive a relation between the fourth moment of the eigenvalue distribution and the variance of the degree distribution, which leads to a sufficient condition for the breakdown of the Wigner semicircle law for dense random networks. Based on the same relation, we propose a classification scheme of the distinct universal behaviors of the spectral density in the dense limit. Our theoretical findings should lead to important insights on the mean-field behavior of models defined on graphs. |
publishDate |
2020 |
dc.date.issued.fl_str_mv |
2020 |
dc.date.accessioned.fl_str_mv |
2021-03-10T04:21:07Z |
dc.type.driver.fl_str_mv |
Estrangeiro info:eu-repo/semantics/article |
dc.type.status.fl_str_mv |
info:eu-repo/semantics/publishedVersion |
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article |
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publishedVersion |
dc.identifier.uri.fl_str_mv |
http://hdl.handle.net/10183/218523 |
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2643-1564 |
dc.identifier.nrb.pt_BR.fl_str_mv |
001122370 |
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2643-1564 001122370 |
url |
http://hdl.handle.net/10183/218523 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.ispartof.pt_BR.fl_str_mv |
Physical Review Research. College Park. Vol. 2, no. 4 (Oct./Dec. 2020), 043116, 12 p. |
dc.rights.driver.fl_str_mv |
info:eu-repo/semantics/openAccess |
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openAccess |
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application/pdf |
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reponame:Repositório Institucional da UFRGS instname:Universidade Federal do Rio Grande do Sul (UFRGS) instacron:UFRGS |
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