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dc.contributor.author
Groisman, Pablo Jose
dc.contributor.author
Soprano Loto, Nahuel
dc.date.available
2021-11-09T13:26:58Z
dc.date.issued
2020-08
dc.identifier.citation
Groisman, Pablo Jose; Soprano Loto, Nahuel; Rank Dependent Branching-Selection Particle Systems; Cornell University; arXiv.org; 8-2020; 1-21
dc.identifier.issn
2331-8422
dc.identifier.uri
http://hdl.handle.net/11336/146415
dc.description.abstract
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.
dc.format
application/pdf
dc.language.iso
eng
dc.publisher
Cornell University
dc.rights
info:eu-repo/semantics/openAccess
dc.rights.uri
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.subject
procesos de ramificación-selección
dc.subject
ecuaciones de reacción-difusion
dc.subject
universalidad
dc.subject.classification
Estadística y Probabilidad
dc.subject.classification
Matemáticas
dc.subject.classification
CIENCIAS NATURALES Y EXACTAS
dc.title
Rank Dependent Branching-Selection Particle Systems
dc.type
info:eu-repo/semantics/article
dc.type
info:ar-repo/semantics/artículo
dc.type
info:eu-repo/semantics/publishedVersion
dc.date.updated
2021-09-07T18:36:32Z
dc.journal.pagination
1-21
dc.journal.pais
Estados Unidos
dc.description.fil
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
dc.description.fil
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
dc.journal.title
arXiv.org
dc.relation.alternativeid
info:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/2008.09460
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