A phase transition for competition interfaces

Autores
Ferrari, Pablo Augusto; Martin, James B.; Pimentel, Leandro P. R.
Año de publicación
2009
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
We study the competition interface between two growing clusters in a growth model associated to last-passage percolation. When the initial unoccupied set is approximately a cone, we show that this interface has an asymptotic direction with probability 1. The behavior of this direction depends on the angle θ of the cone: for θ≥180°, the direction is deterministic, while for θ<180°, it is random, and its distribution can be given explicitly in certain cases. We also obtain partial results on the fluctuations of the interface around its asymptotic direction. The evolution of the competition interface in the growth model can be mapped onto the path of a second-class particle in the totally asymmetric simple exclusion process; from the existence of the limiting direction for the interface, we obtain a new and rather natural proof of the strong law of large numbers (with perhaps a random limit) for the position of the second-class particle at large times.
Fil: Ferrari, Pablo Augusto. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; Argentina
Fil: Martin, James B.. University of Oxford; Reino Unido
Fil: Pimentel, Leandro P. R.. Delft University of Technology; Países Bajos
Materia
ASYMMETRIC SIMPLE EXCLUSION
BURGERS EQUATION
COMPETITION INTERFACE
LAST-PASSAGE PERCOLATION
RAREFACTION FAN
SECOND-CLASS PARTICLE
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:11336/244758
Acceder
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network_name_str CONICET Digital (CONICET)
spelling A phase transition for competition interfacesFerrari, Pablo AugustoMartin, James B.Pimentel, Leandro P. R.ASYMMETRIC SIMPLE EXCLUSIONBURGERS EQUATIONCOMPETITION INTERFACELAST-PASSAGE PERCOLATIONRAREFACTION FANSECOND-CLASS PARTICLEhttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1We study the competition interface between two growing clusters in a growth model associated to last-passage percolation. When the initial unoccupied set is approximately a cone, we show that this interface has an asymptotic direction with probability 1. The behavior of this direction depends on the angle θ of the cone: for θ≥180°, the direction is deterministic, while for θ<180°, it is random, and its distribution can be given explicitly in certain cases. We also obtain partial results on the fluctuations of the interface around its asymptotic direction. The evolution of the competition interface in the growth model can be mapped onto the path of a second-class particle in the totally asymmetric simple exclusion process; from the existence of the limiting direction for the interface, we obtain a new and rather natural proof of the strong law of large numbers (with perhaps a random limit) for the position of the second-class particle at large times.Fil: Ferrari, Pablo Augusto. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; ArgentinaFil: Martin, James B.. University of Oxford; Reino UnidoFil: Pimentel, Leandro P. R.. Delft University of Technology; Países BajosInstitute of Mathematical Statistics2009-12info: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/11336/244758Ferrari, Pablo Augusto; Martin, James B.; Pimentel, Leandro P. R.; A phase transition for competition interfaces; Institute of Mathematical Statistics; Annals Of Applied Probability, The; 19; 1; 12-2009; 281-3171050-5164CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/doi/10.1214/08-AAP542info:eu-repo/semantics/altIdentifier/url/https://projecteuclid.org/journals/annals-of-applied-probability/volume-19/issue-1/A-phase-transition-for-competition-interfaces/10.1214/08-AAP542.fullinfo:eu-repo/semantics/altIdentifier/arxiv/https://arxiv.org/pdf/math/0701418info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-10-22T11:13:17Zoai:ri.conicet.gov.ar:11336/244758instacron: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 11:13:17.635CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv A phase transition for competition interfaces
title A phase transition for competition interfaces
spellingShingle A phase transition for competition interfaces
Ferrari, Pablo Augusto
ASYMMETRIC SIMPLE EXCLUSION
BURGERS EQUATION
COMPETITION INTERFACE
LAST-PASSAGE PERCOLATION
RAREFACTION FAN
SECOND-CLASS PARTICLE
title_short A phase transition for competition interfaces
title_full A phase transition for competition interfaces
title_fullStr A phase transition for competition interfaces
title_full_unstemmed A phase transition for competition interfaces
title_sort A phase transition for competition interfaces
dc.creator.none.fl_str_mv Ferrari, Pablo Augusto
Martin, James B.
Pimentel, Leandro P. R.
author Ferrari, Pablo Augusto
author_facet Ferrari, Pablo Augusto
Martin, James B.
Pimentel, Leandro P. R.
author_role author
author2 Martin, James B.
Pimentel, Leandro P. R.
author2_role author
author
dc.subject.none.fl_str_mv ASYMMETRIC SIMPLE EXCLUSION
BURGERS EQUATION
COMPETITION INTERFACE
LAST-PASSAGE PERCOLATION
RAREFACTION FAN
SECOND-CLASS PARTICLE
topic ASYMMETRIC SIMPLE EXCLUSION
BURGERS EQUATION
COMPETITION INTERFACE
LAST-PASSAGE PERCOLATION
RAREFACTION FAN
SECOND-CLASS PARTICLE
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 study the competition interface between two growing clusters in a growth model associated to last-passage percolation. When the initial unoccupied set is approximately a cone, we show that this interface has an asymptotic direction with probability 1. The behavior of this direction depends on the angle θ of the cone: for θ≥180°, the direction is deterministic, while for θ<180°, it is random, and its distribution can be given explicitly in certain cases. We also obtain partial results on the fluctuations of the interface around its asymptotic direction. The evolution of the competition interface in the growth model can be mapped onto the path of a second-class particle in the totally asymmetric simple exclusion process; from the existence of the limiting direction for the interface, we obtain a new and rather natural proof of the strong law of large numbers (with perhaps a random limit) for the position of the second-class particle at large times.
Fil: Ferrari, Pablo Augusto. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; Argentina
Fil: Martin, James B.. University of Oxford; Reino Unido
Fil: Pimentel, Leandro P. R.. Delft University of Technology; Países Bajos
description We study the competition interface between two growing clusters in a growth model associated to last-passage percolation. When the initial unoccupied set is approximately a cone, we show that this interface has an asymptotic direction with probability 1. The behavior of this direction depends on the angle θ of the cone: for θ≥180°, the direction is deterministic, while for θ<180°, it is random, and its distribution can be given explicitly in certain cases. We also obtain partial results on the fluctuations of the interface around its asymptotic direction. The evolution of the competition interface in the growth model can be mapped onto the path of a second-class particle in the totally asymmetric simple exclusion process; from the existence of the limiting direction for the interface, we obtain a new and rather natural proof of the strong law of large numbers (with perhaps a random limit) for the position of the second-class particle at large times.
publishDate 2009
dc.date.none.fl_str_mv 2009-12
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/11336/244758
Ferrari, Pablo Augusto; Martin, James B.; Pimentel, Leandro P. R.; A phase transition for competition interfaces; Institute of Mathematical Statistics; Annals Of Applied Probability, The; 19; 1; 12-2009; 281-317
1050-5164
CONICET Digital
CONICET
url http://hdl.handle.net/11336/244758
identifier_str_mv Ferrari, Pablo Augusto; Martin, James B.; Pimentel, Leandro P. R.; A phase transition for competition interfaces; Institute of Mathematical Statistics; Annals Of Applied Probability, The; 19; 1; 12-2009; 281-317
1050-5164
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/doi/10.1214/08-AAP542
info:eu-repo/semantics/altIdentifier/url/https://projecteuclid.org/journals/annals-of-applied-probability/volume-19/issue-1/A-phase-transition-for-competition-interfaces/10.1214/08-AAP542.full
info:eu-repo/semantics/altIdentifier/arxiv/https://arxiv.org/pdf/math/0701418
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 Institute of Mathematical Statistics
publisher.none.fl_str_mv Institute of Mathematical Statistics
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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