A probabilistic Approach to polynomial Inequalities

Autores
Pinasco, Damian; Zalduendo, Ignacio Martin
Año de publicación
2012
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
We define a probability measure on the space of polynomials over Rn in order to address questions regarding the attainment of the norm at given points and the validity of polynomial inequalities. Using this measure, we prove that for all degrees k ≥ 3, the probability that a k-homogeneous polynomial attains a local extremum at a vertex of the unit ball of n 1 tends to one as the dimension n increases. We also give bounds for the probability of some general polynomial inequalities.
Fil: Pinasco, Damian. Universidad Torcuato Di Tella. Departamento de Matemáticas y Estadística; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Fil: Zalduendo, Ignacio Martin. Universidad Torcuato Di Tella. Departamento de Matemáticas y Estadística; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Materia
HOMOGENEOUS POLYNOMIALS
GAUSSIAN MEASURE
OPTIMIZATION
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:11336/197247
Acceder
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network_name_str CONICET Digital (CONICET)
spelling A probabilistic Approach to polynomial InequalitiesPinasco, DamianZalduendo, Ignacio MartinHOMOGENEOUS POLYNOMIALSGAUSSIAN MEASUREOPTIMIZATIONhttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1We define a probability measure on the space of polynomials over Rn in order to address questions regarding the attainment of the norm at given points and the validity of polynomial inequalities. Using this measure, we prove that for all degrees k ≥ 3, the probability that a k-homogeneous polynomial attains a local extremum at a vertex of the unit ball of n 1 tends to one as the dimension n increases. We also give bounds for the probability of some general polynomial inequalities.Fil: Pinasco, Damian. Universidad Torcuato Di Tella. Departamento de Matemáticas y Estadística; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Zalduendo, Ignacio Martin. Universidad Torcuato Di Tella. Departamento de Matemáticas y Estadística; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaHebrew Univ Magnes Press2012-08info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/197247Pinasco, Damian; Zalduendo, Ignacio Martin; A probabilistic Approach to polynomial Inequalities; Hebrew Univ Magnes Press; Israel Journal Of Mathematics; 190; 1; 8-2012; 67-820021-21721565-8511CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/https://link.springer.com/article/10.1007/s11856-011-0193-3info:eu-repo/semantics/altIdentifier/doi/10.1007/s11856-011-0193-3info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-10-22T11:28:50Zoai:ri.conicet.gov.ar:11336/197247instacron: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:34982025-10-22 11:28:50.68CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv A probabilistic Approach to polynomial Inequalities
title A probabilistic Approach to polynomial Inequalities
spellingShingle A probabilistic Approach to polynomial Inequalities
Pinasco, Damian
HOMOGENEOUS POLYNOMIALS
GAUSSIAN MEASURE
OPTIMIZATION
title_short A probabilistic Approach to polynomial Inequalities
title_full A probabilistic Approach to polynomial Inequalities
title_fullStr A probabilistic Approach to polynomial Inequalities
title_full_unstemmed A probabilistic Approach to polynomial Inequalities
title_sort A probabilistic Approach to polynomial Inequalities
dc.creator.none.fl_str_mv Pinasco, Damian
Zalduendo, Ignacio Martin
author Pinasco, Damian
author_facet Pinasco, Damian
Zalduendo, Ignacio Martin
author_role author
author2 Zalduendo, Ignacio Martin
author2_role author
dc.subject.none.fl_str_mv HOMOGENEOUS POLYNOMIALS
GAUSSIAN MEASURE
OPTIMIZATION
topic HOMOGENEOUS POLYNOMIALS
GAUSSIAN MEASURE
OPTIMIZATION
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 define a probability measure on the space of polynomials over Rn in order to address questions regarding the attainment of the norm at given points and the validity of polynomial inequalities. Using this measure, we prove that for all degrees k ≥ 3, the probability that a k-homogeneous polynomial attains a local extremum at a vertex of the unit ball of n 1 tends to one as the dimension n increases. We also give bounds for the probability of some general polynomial inequalities.
Fil: Pinasco, Damian. Universidad Torcuato Di Tella. Departamento de Matemáticas y Estadística; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Fil: Zalduendo, Ignacio Martin. Universidad Torcuato Di Tella. Departamento de Matemáticas y Estadística; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
description We define a probability measure on the space of polynomials over Rn in order to address questions regarding the attainment of the norm at given points and the validity of polynomial inequalities. Using this measure, we prove that for all degrees k ≥ 3, the probability that a k-homogeneous polynomial attains a local extremum at a vertex of the unit ball of n 1 tends to one as the dimension n increases. We also give bounds for the probability of some general polynomial inequalities.
publishDate 2012
dc.date.none.fl_str_mv 2012-08
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/11336/197247
Pinasco, Damian; Zalduendo, Ignacio Martin; A probabilistic Approach to polynomial Inequalities; Hebrew Univ Magnes Press; Israel Journal Of Mathematics; 190; 1; 8-2012; 67-82
0021-2172
1565-8511
CONICET Digital
CONICET
url http://hdl.handle.net/11336/197247
identifier_str_mv Pinasco, Damian; Zalduendo, Ignacio Martin; A probabilistic Approach to polynomial Inequalities; Hebrew Univ Magnes Press; Israel Journal Of Mathematics; 190; 1; 8-2012; 67-82
0021-2172
1565-8511
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://link.springer.com/article/10.1007/s11856-011-0193-3
info:eu-repo/semantics/altIdentifier/doi/10.1007/s11856-011-0193-3
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
application/pdf
application/pdf
dc.publisher.none.fl_str_mv Hebrew Univ Magnes Press
publisher.none.fl_str_mv Hebrew Univ Magnes 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 12.982451

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