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
- Institución
- Consejo Nacional de Investigaciones Científicas y Técnicas
- OAI Identificador
- oai:ri.conicet.gov.ar:11336/197247
Ver los metadatos del registro completo
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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 Técnicas2025-09-29T09:59:28Zoai: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:34982025-09-29 09:59:29.237CONICET 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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1844613764591124480 |
score |
13.070432 |