The genealogy of branching brownian motion with absorption
We consider a system of particles which perform branching Brownian motion with negative drift and are killed upon reaching zero, in the nearcritical regime where the total population stays roughly constant with approximately N particles. We show that the characteristic time scale for the evolution o...
| Главные авторы: | , , |
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| Формат: | Journal article |
| Язык: | English |
| Опубликовано: |
2013
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| _version_ | 1826273964807159808 |
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| author | Berestycki, J Berestycki, N Schweinsberg, J |
| author_facet | Berestycki, J Berestycki, N Schweinsberg, J |
| author_sort | Berestycki, J |
| collection | OXFORD |
| description | We consider a system of particles which perform branching Brownian motion with negative drift and are killed upon reaching zero, in the nearcritical regime where the total population stays roughly constant with approximately N particles. We show that the characteristic time scale for the evolution of this population is of order (logN)3, in the sense that when time is measured in these units, the scaled number of particles converges to a variant of Neveu's continuous-state branching process. Furthermore, the genealogy of the particles is then governed by a coalescent process known as the Bolthausen-Sznitman coalescent. This validates the nonrigorous predictions by Brunet, Derrida, Muller and Munier for a closely related model. © Institute of Mathematical Statistics, 2013. |
| first_indexed | 2024-03-06T22:36:14Z |
| format | Journal article |
| id | oxford-uuid:5a003490-aa38-4616-b975-b2f3d91bd62c |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-06T22:36:14Z |
| publishDate | 2013 |
| record_format | dspace |
| spelling | oxford-uuid:5a003490-aa38-4616-b975-b2f3d91bd62c2022-03-26T17:13:02ZThe genealogy of branching brownian motion with absorptionJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:5a003490-aa38-4616-b975-b2f3d91bd62cEnglishSymplectic Elements at Oxford2013Berestycki, JBerestycki, NSchweinsberg, JWe consider a system of particles which perform branching Brownian motion with negative drift and are killed upon reaching zero, in the nearcritical regime where the total population stays roughly constant with approximately N particles. We show that the characteristic time scale for the evolution of this population is of order (logN)3, in the sense that when time is measured in these units, the scaled number of particles converges to a variant of Neveu's continuous-state branching process. Furthermore, the genealogy of the particles is then governed by a coalescent process known as the Bolthausen-Sznitman coalescent. This validates the nonrigorous predictions by Brunet, Derrida, Muller and Munier for a closely related model. © Institute of Mathematical Statistics, 2013. |
| spellingShingle | Berestycki, J Berestycki, N Schweinsberg, J The genealogy of branching brownian motion with absorption |
| title | The genealogy of branching brownian motion with absorption |
| title_full | The genealogy of branching brownian motion with absorption |
| title_fullStr | The genealogy of branching brownian motion with absorption |
| title_full_unstemmed | The genealogy of branching brownian motion with absorption |
| title_short | The genealogy of branching brownian motion with absorption |
| title_sort | genealogy of branching brownian motion with absorption |
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