Energy and discrepancy of rotationally invariant determinantal point processes in high dimensional spheres

We study expected Riesz s-energies and linear statistics of some determinantal processes on the sphere $\mathbb{S}^{d}$. In particular, we compute the expected Riesz and logarithmic energies of the determinantal processes given by the reproducing kernel of the space of spherical harmonics. This kern...

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Autores: Beltrán, Carlos, Marzo Sánchez, Jordi, Ortega Cerdà, Joaquim
Tipo de recurso: artículo
Estado:Versión aceptada para publicación
Fecha de publicación:2016
País:España
Institución:Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya)
Repositorio:Recercat. Dipósit de la Recerca de Catalunya
OAI Identifier:oai:recercat.cat:2445/102303
Acceso en línea:https://hdl.handle.net/2445/102303
Access Level:acceso abierto
Palabra clave:Funcions hipergeomètriques
Teoria de nombres
Hypergeometric functions
Number theory
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spelling Energy and discrepancy of rotationally invariant determinantal point processes in high dimensional spheresBeltrán, CarlosMarzo Sánchez, JordiOrtega Cerdà, JoaquimFuncions hipergeomètriquesTeoria de nombresHypergeometric functionsNumber theoryWe study expected Riesz s-energies and linear statistics of some determinantal processes on the sphere $\mathbb{S}^{d}$. In particular, we compute the expected Riesz and logarithmic energies of the determinantal processes given by the reproducing kernel of the space of spherical harmonics. This kernel defines the so called harmonic ensemble on $\mathbb{S}^{d}$. With these computations we improve previous estimates for the discrete minimal energy of configurations of points in the sphere. We prove a comparison result for Riesz 2-energies of points defined through determinantal point processes associated with isotropic kernels. As a corollary we get that the Riesz 2-energy of the harmonic ensemble is optimal among ensembles defined by isotropic kernels with the same trace. Finally, we study the variance of smooth and rough linear statistics for the harmonic ensemble and compare the results with the variance for the spherical ensemble (in $\mathbb{S}^{d}$).Elsevier2016201820162016info:eu-repo/semantics/articleinfo:eu-repo/semantics/acceptedVersion34 p.application/pdfapplication/pdfhttps://hdl.handle.net/2445/102303Articles publicats en revistes (Matemàtiques i Informàtica)reponame:Recercat. Dipósit de la Recerca de Catalunyainstname:Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya)InglésVersió postprint del document publicat a: http://dx.doi.org/10.1016/j.jco.2016.08.001Journal of Complexity, 2016, vol. 37, p. 76-109http://dx.doi.org/10.1016/j.jco.2016.08.001cc-by-nc-nd (c) Academic Press, 2016http://creativecommons.org/licenses/by-nc-nd/3.0/esinfo:eu-repo/semantics/openAccessoai:recercat.cat:2445/1023032026-05-29T05:05:01Z
dc.title.none.fl_str_mv Energy and discrepancy of rotationally invariant determinantal point processes in high dimensional spheres
title Energy and discrepancy of rotationally invariant determinantal point processes in high dimensional spheres
spellingShingle Energy and discrepancy of rotationally invariant determinantal point processes in high dimensional spheres
Beltrán, Carlos
Funcions hipergeomètriques
Teoria de nombres
Hypergeometric functions
Number theory
title_short Energy and discrepancy of rotationally invariant determinantal point processes in high dimensional spheres
title_full Energy and discrepancy of rotationally invariant determinantal point processes in high dimensional spheres
title_fullStr Energy and discrepancy of rotationally invariant determinantal point processes in high dimensional spheres
title_full_unstemmed Energy and discrepancy of rotationally invariant determinantal point processes in high dimensional spheres
title_sort Energy and discrepancy of rotationally invariant determinantal point processes in high dimensional spheres
dc.creator.none.fl_str_mv Beltrán, Carlos
Marzo Sánchez, Jordi
Ortega Cerdà, Joaquim
author Beltrán, Carlos
author_facet Beltrán, Carlos
Marzo Sánchez, Jordi
Ortega Cerdà, Joaquim
author_role author
author2 Marzo Sánchez, Jordi
Ortega Cerdà, Joaquim
author2_role author
author
dc.subject.none.fl_str_mv Funcions hipergeomètriques
Teoria de nombres
Hypergeometric functions
Number theory
topic Funcions hipergeomètriques
Teoria de nombres
Hypergeometric functions
Number theory
description We study expected Riesz s-energies and linear statistics of some determinantal processes on the sphere $\mathbb{S}^{d}$. In particular, we compute the expected Riesz and logarithmic energies of the determinantal processes given by the reproducing kernel of the space of spherical harmonics. This kernel defines the so called harmonic ensemble on $\mathbb{S}^{d}$. With these computations we improve previous estimates for the discrete minimal energy of configurations of points in the sphere. We prove a comparison result for Riesz 2-energies of points defined through determinantal point processes associated with isotropic kernels. As a corollary we get that the Riesz 2-energy of the harmonic ensemble is optimal among ensembles defined by isotropic kernels with the same trace. Finally, we study the variance of smooth and rough linear statistics for the harmonic ensemble and compare the results with the variance for the spherical ensemble (in $\mathbb{S}^{d}$).
publishDate 2016
dc.date.none.fl_str_mv 2016
2016
2016
2018
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/acceptedVersion
format article
status_str acceptedVersion
dc.identifier.none.fl_str_mv https://hdl.handle.net/2445/102303
url https://hdl.handle.net/2445/102303
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv Versió postprint del document publicat a: http://dx.doi.org/10.1016/j.jco.2016.08.001
Journal of Complexity, 2016, vol. 37, p. 76-109
http://dx.doi.org/10.1016/j.jco.2016.08.001
dc.rights.none.fl_str_mv cc-by-nc-nd (c) Academic Press, 2016
http://creativecommons.org/licenses/by-nc-nd/3.0/es
info:eu-repo/semantics/openAccess
rights_invalid_str_mv cc-by-nc-nd (c) Academic Press, 2016
http://creativecommons.org/licenses/by-nc-nd/3.0/es
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv 34 p.
application/pdf
application/pdf
dc.publisher.none.fl_str_mv Elsevier
publisher.none.fl_str_mv Elsevier
dc.source.none.fl_str_mv Articles publicats en revistes (Matemàtiques i Informàtica)
reponame:Recercat. Dipósit de la Recerca de Catalunya
instname:Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya)
instname_str Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya)
reponame_str Recercat. Dipósit de la Recerca de Catalunya
collection Recercat. Dipósit de la Recerca de Catalunya
repository.name.fl_str_mv
repository.mail.fl_str_mv
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score 15,812429

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