Non-intersecting squared Bessel paths with one positive starting and ending point

Autores
Delvaux, Steven; Kuijlaars, Arno B. J.; Román, Pablo Manuel; Zhang, Lun
Año de publicación
2012
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
We consider a model of n non-intersecting squared Bessel processes with one starting point a > 0 at time t = 0 and one ending point b > 0 at time t = T. After proper scaling, the paths fill out a region in the tx-plane. The region may come to the hard edge at 0 or may not, depending on the value of the product ab. We formulate a vector equilibrium problem for this model, which is defined for three measures, with upper constraints on the first and third measures and an external field on the second measure. It is shown that the limiting mean distribution of the paths at time t is given by the second component of the vector that minimizes this vector equilibrium problem. The proof is based on a steepest descent analysis for a 4 × 4 matrix-valued Riemann-Hilbert problem which characterizes the correlation kernel of the paths at time t. We also discuss the precise locations of the phase transitions.
Fil: Delvaux, Steven. Katholikie Universiteit Leuven; Bélgica
Fil: Kuijlaars, Arno B. J.. Katholikie Universiteit Leuven; Bélgica
Fil: Román, Pablo Manuel. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Centro de Investigación y Estudios de Matemática. Universidad Nacional de Córdoba. Centro de Investigación y Estudios de Matemática; Argentina. Katholikie Universiteit Leuven; Bélgica
Fil: Zhang, Lun. Katholikie Universiteit Leuven; Bélgica
Materia
Non-intersecting Bessel squared paths
Multiple orthogonal polynomials
Phase transitions
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:11336/268693
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/268693
network_acronym_str CONICETDig
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network_name_str CONICET Digital (CONICET)
spelling Non-intersecting squared Bessel paths with one positive starting and ending pointDelvaux, StevenKuijlaars, Arno B. J.Román, Pablo ManuelZhang, LunNon-intersecting Bessel squared pathsMultiple orthogonal polynomialsPhase transitionshttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1We consider a model of n non-intersecting squared Bessel processes with one starting point a > 0 at time t = 0 and one ending point b > 0 at time t = T. After proper scaling, the paths fill out a region in the tx-plane. The region may come to the hard edge at 0 or may not, depending on the value of the product ab. We formulate a vector equilibrium problem for this model, which is defined for three measures, with upper constraints on the first and third measures and an external field on the second measure. It is shown that the limiting mean distribution of the paths at time t is given by the second component of the vector that minimizes this vector equilibrium problem. The proof is based on a steepest descent analysis for a 4 × 4 matrix-valued Riemann-Hilbert problem which characterizes the correlation kernel of the paths at time t. We also discuss the precise locations of the phase transitions.Fil: Delvaux, Steven. Katholikie Universiteit Leuven; BélgicaFil: Kuijlaars, Arno B. J.. Katholikie Universiteit Leuven; BélgicaFil: Román, Pablo Manuel. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Centro de Investigación y Estudios de Matemática. Universidad Nacional de Córdoba. Centro de Investigación y Estudios de Matemática; Argentina. Katholikie Universiteit Leuven; BélgicaFil: Zhang, Lun. Katholikie Universiteit Leuven; BélgicaSpringer2012-08info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/268693Delvaux, Steven; Kuijlaars, Arno B. J.; Román, Pablo Manuel; Zhang, Lun; Non-intersecting squared Bessel paths with one positive starting and ending point; Springer; Journal d'Analyse Mathématique; 118; 1; 8-2012; 105-1590021-7670CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/https://link.springer.com/article/10.1007/s11854-012-0031-5info:eu-repo/semantics/altIdentifier/doi/10.1007/s11854-012-0031-5info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-29T10:44:33Zoai:ri.conicet.gov.ar:11336/268693instacron: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 10:44:34.263CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Non-intersecting squared Bessel paths with one positive starting and ending point
title Non-intersecting squared Bessel paths with one positive starting and ending point
spellingShingle Non-intersecting squared Bessel paths with one positive starting and ending point
Delvaux, Steven
Non-intersecting Bessel squared paths
Multiple orthogonal polynomials
Phase transitions
title_short Non-intersecting squared Bessel paths with one positive starting and ending point
title_full Non-intersecting squared Bessel paths with one positive starting and ending point
title_fullStr Non-intersecting squared Bessel paths with one positive starting and ending point
title_full_unstemmed Non-intersecting squared Bessel paths with one positive starting and ending point
title_sort Non-intersecting squared Bessel paths with one positive starting and ending point
dc.creator.none.fl_str_mv Delvaux, Steven
Kuijlaars, Arno B. J.
Román, Pablo Manuel
Zhang, Lun
author Delvaux, Steven
author_facet Delvaux, Steven
Kuijlaars, Arno B. J.
Román, Pablo Manuel
Zhang, Lun
author_role author
author2 Kuijlaars, Arno B. J.
Román, Pablo Manuel
Zhang, Lun
author2_role author
author
author
dc.subject.none.fl_str_mv Non-intersecting Bessel squared paths
Multiple orthogonal polynomials
Phase transitions
topic Non-intersecting Bessel squared paths
Multiple orthogonal polynomials
Phase transitions
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 consider a model of n non-intersecting squared Bessel processes with one starting point a > 0 at time t = 0 and one ending point b > 0 at time t = T. After proper scaling, the paths fill out a region in the tx-plane. The region may come to the hard edge at 0 or may not, depending on the value of the product ab. We formulate a vector equilibrium problem for this model, which is defined for three measures, with upper constraints on the first and third measures and an external field on the second measure. It is shown that the limiting mean distribution of the paths at time t is given by the second component of the vector that minimizes this vector equilibrium problem. The proof is based on a steepest descent analysis for a 4 × 4 matrix-valued Riemann-Hilbert problem which characterizes the correlation kernel of the paths at time t. We also discuss the precise locations of the phase transitions.
Fil: Delvaux, Steven. Katholikie Universiteit Leuven; Bélgica
Fil: Kuijlaars, Arno B. J.. Katholikie Universiteit Leuven; Bélgica
Fil: Román, Pablo Manuel. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Centro de Investigación y Estudios de Matemática. Universidad Nacional de Córdoba. Centro de Investigación y Estudios de Matemática; Argentina. Katholikie Universiteit Leuven; Bélgica
Fil: Zhang, Lun. Katholikie Universiteit Leuven; Bélgica
description We consider a model of n non-intersecting squared Bessel processes with one starting point a > 0 at time t = 0 and one ending point b > 0 at time t = T. After proper scaling, the paths fill out a region in the tx-plane. The region may come to the hard edge at 0 or may not, depending on the value of the product ab. We formulate a vector equilibrium problem for this model, which is defined for three measures, with upper constraints on the first and third measures and an external field on the second measure. It is shown that the limiting mean distribution of the paths at time t is given by the second component of the vector that minimizes this vector equilibrium problem. The proof is based on a steepest descent analysis for a 4 × 4 matrix-valued Riemann-Hilbert problem which characterizes the correlation kernel of the paths at time t. We also discuss the precise locations of the phase transitions.
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/11336/268693
Delvaux, Steven; Kuijlaars, Arno B. J.; Román, Pablo Manuel; Zhang, Lun; Non-intersecting squared Bessel paths with one positive starting and ending point; Springer; Journal d'Analyse Mathématique; 118; 1; 8-2012; 105-159
0021-7670
CONICET Digital
CONICET
url http://hdl.handle.net/11336/268693
identifier_str_mv Delvaux, Steven; Kuijlaars, Arno B. J.; Román, Pablo Manuel; Zhang, Lun; Non-intersecting squared Bessel paths with one positive starting and ending point; Springer; Journal d'Analyse Mathématique; 118; 1; 8-2012; 105-159
0021-7670
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/s11854-012-0031-5
info:eu-repo/semantics/altIdentifier/doi/10.1007/s11854-012-0031-5
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
dc.publisher.none.fl_str_mv Springer
publisher.none.fl_str_mv Springer
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 13.070432

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