Rank Dependent Branching-Selection Particle Systems

Autores
Groisman, Pablo Jose; Soprano Loto, Nahuel
Año de publicación
2020
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
We consider a large family of branching-selection particle systems. Thebranching rate of each particle depends on its rank and is given by a functionb defined on the unit interval. There is also a killing measure D supportedon the unit interval as well. At branching times, a particle is chosen amongall particles to the left of the branching one by sampling its rank accordingto D. The measure D is allowed to have total mass less than one, whichcorresponds to a positive probability of no killing. Between branching times,particles perform independent Brownian Motions in the real line. This settingincludes several well known models like Branching Brownian Motion (BBM),N-BBM, rank dependent BBM, and many others. We conjecture a scaling limit forthis class of processes and prove such a limit for a related class ofbranching-selection particle system. This family is rich enough to allow us touse the behavior of solutions of the limiting equation to prove the asymptoticvelocity of the rightmost particle under minimal conditions on b and D. Thebehavior turns out to be universal and depends only on b(1) and the totalmass of D. If the total mass is one, the number of particles in the systemN is conserved and the velocities vN converge to 2b(1)‾‾‾‾‾√. When thetotal mass of D is less than one, the number of particles in the system growsup in time exponentially fast and the asymptotic velocity of the rightmost oneis 2b(1)‾‾‾‾‾√ independently of the number of initial particles.
Fil: Groisman, Pablo Jose. 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: Soprano Loto, Nahuel. 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
Materia
procesos de ramificación-selección
ecuaciones de reacción-difusion
universalidad
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:11336/146415
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/146415
network_acronym_str CONICETDig
repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling Rank Dependent Branching-Selection Particle SystemsGroisman, Pablo JoseSoprano Loto, Nahuelprocesos de ramificación-selecciónecuaciones de reacción-difusionuniversalidadhttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1We consider a large family of branching-selection particle systems. Thebranching rate of each particle depends on its rank and is given by a functionb defined on the unit interval. There is also a killing measure D supportedon the unit interval as well. At branching times, a particle is chosen amongall particles to the left of the branching one by sampling its rank accordingto D. The measure D is allowed to have total mass less than one, whichcorresponds to a positive probability of no killing. Between branching times,particles perform independent Brownian Motions in the real line. This settingincludes several well known models like Branching Brownian Motion (BBM),N-BBM, rank dependent BBM, and many others. We conjecture a scaling limit forthis class of processes and prove such a limit for a related class ofbranching-selection particle system. This family is rich enough to allow us touse the behavior of solutions of the limiting equation to prove the asymptoticvelocity of the rightmost particle under minimal conditions on b and D. Thebehavior turns out to be universal and depends only on b(1) and the totalmass of D. If the total mass is one, the number of particles in the systemN is conserved and the velocities vN converge to 2b(1)‾‾‾‾‾√. When thetotal mass of D is less than one, the number of particles in the system growsup in time exponentially fast and the asymptotic velocity of the rightmost oneis 2b(1)‾‾‾‾‾√ independently of the number of initial particles.Fil: Groisman, Pablo Jose. 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: Soprano Loto, Nahuel. 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"; ArgentinaCornell University2020-08info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/146415Groisman, Pablo Jose; Soprano Loto, Nahuel; Rank Dependent Branching-Selection Particle Systems; Cornell University; arXiv.org; 8-2020; 1-212331-8422CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/2008.09460info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-10-22T12:18:11Zoai:ri.conicet.gov.ar:11336/146415instacron: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 12:18:12.173CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Rank Dependent Branching-Selection Particle Systems
title Rank Dependent Branching-Selection Particle Systems
spellingShingle Rank Dependent Branching-Selection Particle Systems
Groisman, Pablo Jose
procesos de ramificación-selección
ecuaciones de reacción-difusion
universalidad
title_short Rank Dependent Branching-Selection Particle Systems
title_full Rank Dependent Branching-Selection Particle Systems
title_fullStr Rank Dependent Branching-Selection Particle Systems
title_full_unstemmed Rank Dependent Branching-Selection Particle Systems
title_sort Rank Dependent Branching-Selection Particle Systems
dc.creator.none.fl_str_mv Groisman, Pablo Jose
Soprano Loto, Nahuel
author Groisman, Pablo Jose
author_facet Groisman, Pablo Jose
Soprano Loto, Nahuel
author_role author
author2 Soprano Loto, Nahuel
author2_role author
dc.subject.none.fl_str_mv procesos de ramificación-selección
ecuaciones de reacción-difusion
universalidad
topic procesos de ramificación-selección
ecuaciones de reacción-difusion
universalidad
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 large family of branching-selection particle systems. Thebranching rate of each particle depends on its rank and is given by a functionb defined on the unit interval. There is also a killing measure D supportedon the unit interval as well. At branching times, a particle is chosen amongall particles to the left of the branching one by sampling its rank accordingto D. The measure D is allowed to have total mass less than one, whichcorresponds to a positive probability of no killing. Between branching times,particles perform independent Brownian Motions in the real line. This settingincludes several well known models like Branching Brownian Motion (BBM),N-BBM, rank dependent BBM, and many others. We conjecture a scaling limit forthis class of processes and prove such a limit for a related class ofbranching-selection particle system. This family is rich enough to allow us touse the behavior of solutions of the limiting equation to prove the asymptoticvelocity of the rightmost particle under minimal conditions on b and D. Thebehavior turns out to be universal and depends only on b(1) and the totalmass of D. If the total mass is one, the number of particles in the systemN is conserved and the velocities vN converge to 2b(1)‾‾‾‾‾√. When thetotal mass of D is less than one, the number of particles in the system growsup in time exponentially fast and the asymptotic velocity of the rightmost oneis 2b(1)‾‾‾‾‾√ independently of the number of initial particles.
Fil: Groisman, Pablo Jose. 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: Soprano Loto, Nahuel. 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
description We consider a large family of branching-selection particle systems. Thebranching rate of each particle depends on its rank and is given by a functionb defined on the unit interval. There is also a killing measure D supportedon the unit interval as well. At branching times, a particle is chosen amongall particles to the left of the branching one by sampling its rank accordingto D. The measure D is allowed to have total mass less than one, whichcorresponds to a positive probability of no killing. Between branching times,particles perform independent Brownian Motions in the real line. This settingincludes several well known models like Branching Brownian Motion (BBM),N-BBM, rank dependent BBM, and many others. We conjecture a scaling limit forthis class of processes and prove such a limit for a related class ofbranching-selection particle system. This family is rich enough to allow us touse the behavior of solutions of the limiting equation to prove the asymptoticvelocity of the rightmost particle under minimal conditions on b and D. Thebehavior turns out to be universal and depends only on b(1) and the totalmass of D. If the total mass is one, the number of particles in the systemN is conserved and the velocities vN converge to 2b(1)‾‾‾‾‾√. When thetotal mass of D is less than one, the number of particles in the system growsup in time exponentially fast and the asymptotic velocity of the rightmost oneis 2b(1)‾‾‾‾‾√ independently of the number of initial particles.
publishDate 2020
dc.date.none.fl_str_mv 2020-08
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/11336/146415
Groisman, Pablo Jose; Soprano Loto, Nahuel; Rank Dependent Branching-Selection Particle Systems; Cornell University; arXiv.org; 8-2020; 1-21
2331-8422
CONICET Digital
CONICET
url http://hdl.handle.net/11336/146415
identifier_str_mv Groisman, Pablo Jose; Soprano Loto, Nahuel; Rank Dependent Branching-Selection Particle Systems; Cornell University; arXiv.org; 8-2020; 1-21
2331-8422
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://arxiv.org/abs/2008.09460
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 Cornell University
publisher.none.fl_str_mv Cornell University
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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