Collision probabilities in the rarefaction fan of asymmetric exclusion processes

Autores
Ferrari, Pablo Augusto; Goncalves, Patricia; Martin, James B.
Año de publicación
2009
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
We consider the one-dimensional asymmetric simple exclusion process (ASEP) in which particles jump to the right at rate p∈(1/2,1] and to the left at rate 1-p, interacting by exclusion. In the initial state there is a finite region such that to the left of this region all sites are occupied and to the right of it all sites are empty. Under this initial state, the hydrodynamical limit of the process converges to the rarefaction fan of the associated Burgers equation. In particular suppose that the initial state has first-class particles to the left of the origin, second-class particles at sites 0 and 1, and holes to the right of site 1. We show that the probability that the two second-class particles eventually collide is (1+p)/3p, where a_collision_ occurs when one of the particles attempts to jump over the other. This also corresponds to the probability that two ASEP processes, started from appropriate initial states and coupled using the so-called "basic coupling", eventually reach the same state. We give various other results about the behaviour of second-class particles in the ASEP. In the totally asymmetric case (p=1) we explain a further representation in terms of a multi-type particle system, and also use the collision result to derive the probability of coexistence of both clusters in a two-type version of the corner growth model.
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: Goncalves, Patricia. Universidade de Sao Paulo; Brasil
Fil: Martin, James B.. University of Oxford; Reino Unido
Materia
competition interfaces
ASYMMETRIC SIMPLE EXCLUSION PROCESS
GROWTH MODEL
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:11336/282939
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/282939
network_acronym_str CONICETDig
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network_name_str CONICET Digital (CONICET)
spelling Collision probabilities in the rarefaction fan of asymmetric exclusion processesFerrari, Pablo AugustoGoncalves, PatriciaMartin, James B.competition interfacesASYMMETRIC SIMPLE EXCLUSION PROCESSGROWTH MODELRAREFACTION FANSECOND-CLASS PARTICLEhttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1We consider the one-dimensional asymmetric simple exclusion process (ASEP) in which particles jump to the right at rate p∈(1/2,1] and to the left at rate 1-p, interacting by exclusion. In the initial state there is a finite region such that to the left of this region all sites are occupied and to the right of it all sites are empty. Under this initial state, the hydrodynamical limit of the process converges to the rarefaction fan of the associated Burgers equation. In particular suppose that the initial state has first-class particles to the left of the origin, second-class particles at sites 0 and 1, and holes to the right of site 1. We show that the probability that the two second-class particles eventually collide is (1+p)/3p, where a_collision_ occurs when one of the particles attempts to jump over the other. This also corresponds to the probability that two ASEP processes, started from appropriate initial states and coupled using the so-called "basic coupling", eventually reach the same state. We give various other results about the behaviour of second-class particles in the ASEP. In the totally asymmetric case (p=1) we explain a further representation in terms of a multi-type particle system, and also use the collision result to derive the probability of coexistence of both clusters in a two-type version of the corner growth model.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: Goncalves, Patricia. Universidade de Sao Paulo; BrasilFil: Martin, James B.. University of Oxford; Reino UnidoInstitute of Mathematical Statistics2009-12info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/282939Ferrari, Pablo Augusto; Goncalves, Patricia; Martin, James B.; Collision probabilities in the rarefaction fan of asymmetric exclusion processes; Institute of Mathematical Statistics; Annales de L'institut Henri Poincare-probabilites Et Statistiques; 45; 4; 12-2009; 1048-10640246-0203CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/http://projecteuclid.org/euclid.aihp/1257529891info:eu-repo/semantics/altIdentifier/doi/10.1214/08-AIHP303info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2026-08-25T14:33:29Zoai:ri.conicet.gov.ar:11336/282939instacron: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:34982026-08-25 14:33:30.103CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Collision probabilities in the rarefaction fan of asymmetric exclusion processes
title Collision probabilities in the rarefaction fan of asymmetric exclusion processes
spellingShingle Collision probabilities in the rarefaction fan of asymmetric exclusion processes
Ferrari, Pablo Augusto
competition interfaces
ASYMMETRIC SIMPLE EXCLUSION PROCESS
GROWTH MODEL
RAREFACTION FAN
SECOND-CLASS PARTICLE
title_short Collision probabilities in the rarefaction fan of asymmetric exclusion processes
title_full Collision probabilities in the rarefaction fan of asymmetric exclusion processes
title_fullStr Collision probabilities in the rarefaction fan of asymmetric exclusion processes
title_full_unstemmed Collision probabilities in the rarefaction fan of asymmetric exclusion processes
title_sort Collision probabilities in the rarefaction fan of asymmetric exclusion processes
dc.creator.none.fl_str_mv Ferrari, Pablo Augusto
Goncalves, Patricia
Martin, James B.
author Ferrari, Pablo Augusto
author_facet Ferrari, Pablo Augusto
Goncalves, Patricia
Martin, James B.
author_role author
author2 Goncalves, Patricia
Martin, James B.
author2_role author
author
dc.subject.none.fl_str_mv competition interfaces
ASYMMETRIC SIMPLE EXCLUSION PROCESS
GROWTH MODEL
RAREFACTION FAN
SECOND-CLASS PARTICLE
topic competition interfaces
ASYMMETRIC SIMPLE EXCLUSION PROCESS
GROWTH MODEL
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 consider the one-dimensional asymmetric simple exclusion process (ASEP) in which particles jump to the right at rate p∈(1/2,1] and to the left at rate 1-p, interacting by exclusion. In the initial state there is a finite region such that to the left of this region all sites are occupied and to the right of it all sites are empty. Under this initial state, the hydrodynamical limit of the process converges to the rarefaction fan of the associated Burgers equation. In particular suppose that the initial state has first-class particles to the left of the origin, second-class particles at sites 0 and 1, and holes to the right of site 1. We show that the probability that the two second-class particles eventually collide is (1+p)/3p, where a_collision_ occurs when one of the particles attempts to jump over the other. This also corresponds to the probability that two ASEP processes, started from appropriate initial states and coupled using the so-called "basic coupling", eventually reach the same state. We give various other results about the behaviour of second-class particles in the ASEP. In the totally asymmetric case (p=1) we explain a further representation in terms of a multi-type particle system, and also use the collision result to derive the probability of coexistence of both clusters in a two-type version of the corner growth model.
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: Goncalves, Patricia. Universidade de Sao Paulo; Brasil
Fil: Martin, James B.. University of Oxford; Reino Unido
description We consider the one-dimensional asymmetric simple exclusion process (ASEP) in which particles jump to the right at rate p∈(1/2,1] and to the left at rate 1-p, interacting by exclusion. In the initial state there is a finite region such that to the left of this region all sites are occupied and to the right of it all sites are empty. Under this initial state, the hydrodynamical limit of the process converges to the rarefaction fan of the associated Burgers equation. In particular suppose that the initial state has first-class particles to the left of the origin, second-class particles at sites 0 and 1, and holes to the right of site 1. We show that the probability that the two second-class particles eventually collide is (1+p)/3p, where a_collision_ occurs when one of the particles attempts to jump over the other. This also corresponds to the probability that two ASEP processes, started from appropriate initial states and coupled using the so-called "basic coupling", eventually reach the same state. We give various other results about the behaviour of second-class particles in the ASEP. In the totally asymmetric case (p=1) we explain a further representation in terms of a multi-type particle system, and also use the collision result to derive the probability of coexistence of both clusters in a two-type version of the corner growth model.
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/11336/282939
Ferrari, Pablo Augusto; Goncalves, Patricia; Martin, James B.; Collision probabilities in the rarefaction fan of asymmetric exclusion processes; Institute of Mathematical Statistics; Annales de L'institut Henri Poincare-probabilites Et Statistiques; 45; 4; 12-2009; 1048-1064
0246-0203
CONICET Digital
CONICET
url http://hdl.handle.net/11336/282939
identifier_str_mv Ferrari, Pablo Augusto; Goncalves, Patricia; Martin, James B.; Collision probabilities in the rarefaction fan of asymmetric exclusion processes; Institute of Mathematical Statistics; Annales de L'institut Henri Poincare-probabilites Et Statistiques; 45; 4; 12-2009; 1048-1064
0246-0203
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/url/http://projecteuclid.org/euclid.aihp/1257529891
info:eu-repo/semantics/altIdentifier/doi/10.1214/08-AIHP303
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
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
_version_ 1874774164931346432
score 13.265058

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