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
- Institución
- Consejo Nacional de Investigaciones Científicas y Técnicas
- OAI Identificador
- oai:ri.conicet.gov.ar:11336/146415
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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 Técnicas2025-09-29T10:44:54Zoai: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:34982025-09-29 10:44:55.278CONICET 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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1844614487865294848 |
score |
13.070432 |