Condensation in Fleming--Viot particle systems with fast selection mechanism
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866910510065123328 |
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| author | Journel, Lucas Lelièvre, Tony Reygner, Julien |
| author_facet | Journel, Lucas Lelièvre, Tony Reygner, Julien |
| contents | We study the Fleming--Viot particle system in a discrete state space, in the regime of a fast selection mechanism, namely with killing rates which grow to infinity. This asymptotics creates a time scale separation which results in the formation of a condensate of all particles, which then evolves according to a continuous-time Markov chain with jump rates depending in a nontrivial way on both the underlying mutation dynamics and the relative speed of growth to infinity of the killing rate between neighbouring sites. We prove the convergence of the particle system and completely describe the dynamics of the condensate in the case where the number of particles is kept fixed, and partially in the case when the number of particles goes to infinity together with (but slower than) the minimal killing rate. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_02054 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Condensation in Fleming--Viot particle systems with fast selection mechanism Journel, Lucas Lelièvre, Tony Reygner, Julien Probability 60J27 60J80 60F99 We study the Fleming--Viot particle system in a discrete state space, in the regime of a fast selection mechanism, namely with killing rates which grow to infinity. This asymptotics creates a time scale separation which results in the formation of a condensate of all particles, which then evolves according to a continuous-time Markov chain with jump rates depending in a nontrivial way on both the underlying mutation dynamics and the relative speed of growth to infinity of the killing rate between neighbouring sites. We prove the convergence of the particle system and completely describe the dynamics of the condensate in the case where the number of particles is kept fixed, and partially in the case when the number of particles goes to infinity together with (but slower than) the minimal killing rate. |
| title | Condensation in Fleming--Viot particle systems with fast selection mechanism |
| topic | Probability 60J27 60J80 60F99 |
| url | https://arxiv.org/abs/2407.02054 |