Brownian bees in the infinite swarm limit
The Brownian bees model is a branching particle system with spatial selection. It is a system of N particles which move as independent Brownian motions in Rd and independently branch at rate 1, and, crucially, at each branching event, the particle which is the furthest away from the origin is remove...
| Autors principals: | , , , |
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| Format: | Journal article |
| Idioma: | English |
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Institute of Mathematical Statistics
2022
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| _version_ | 1826312444552675328 |
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| author | Berestycki, J Brunet, E Nolen, J Penington, S |
| author_facet | Berestycki, J Brunet, E Nolen, J Penington, S |
| author_sort | Berestycki, J |
| collection | OXFORD |
| description | The Brownian bees model is a branching particle system with spatial selection. It is a system of N particles which move as independent Brownian motions in Rd and independently branch at rate 1, and, crucially, at each branching event, the particle which is the furthest away from the origin is removed to keep the population size constant. In the present work we prove that, as N→∞, the behaviour of the particle system is well approximated by the solution of a free boundary problem (which is the subject of a companion paper (Trans. Amer. Math. Soc. 374 (2021) 6269–6329)), the hydrodynamic limit of the system. We then show that for this model the so-called selection principle holds; that is, that as N→∞, the equilibrium density of the particle system converges to the steady-state solution of the free boundary problem. |
| first_indexed | 2024-03-07T08:11:00Z |
| format | Journal article |
| id | oxford-uuid:5bedbe39-f180-4e13-a25e-3ad723e5f47c |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-04-09T03:54:40Z |
| publishDate | 2022 |
| publisher | Institute of Mathematical Statistics |
| record_format | dspace |
| spelling | oxford-uuid:5bedbe39-f180-4e13-a25e-3ad723e5f47c2024-03-07T11:49:08ZBrownian bees in the infinite swarm limitJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:5bedbe39-f180-4e13-a25e-3ad723e5f47cEnglishSymplectic ElementsInstitute of Mathematical Statistics2022Berestycki, JBrunet, ENolen, JPenington, SThe Brownian bees model is a branching particle system with spatial selection. It is a system of N particles which move as independent Brownian motions in Rd and independently branch at rate 1, and, crucially, at each branching event, the particle which is the furthest away from the origin is removed to keep the population size constant. In the present work we prove that, as N→∞, the behaviour of the particle system is well approximated by the solution of a free boundary problem (which is the subject of a companion paper (Trans. Amer. Math. Soc. 374 (2021) 6269–6329)), the hydrodynamic limit of the system. We then show that for this model the so-called selection principle holds; that is, that as N→∞, the equilibrium density of the particle system converges to the steady-state solution of the free boundary problem. |
| spellingShingle | Berestycki, J Brunet, E Nolen, J Penington, S Brownian bees in the infinite swarm limit |
| title | Brownian bees in the infinite swarm limit |
| title_full | Brownian bees in the infinite swarm limit |
| title_fullStr | Brownian bees in the infinite swarm limit |
| title_full_unstemmed | Brownian bees in the infinite swarm limit |
| title_short | Brownian bees in the infinite swarm limit |
| title_sort | brownian bees in the infinite swarm limit |
| work_keys_str_mv | AT berestyckij brownianbeesintheinfiniteswarmlimit AT brunete brownianbeesintheinfiniteswarmlimit AT nolenj brownianbeesintheinfiniteswarmlimit AT peningtons brownianbeesintheinfiniteswarmlimit |