Uniform-in-time propagation of chaos for the Cucker--Smale model
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866909878933520384 |
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| author | Gerber, Nicolai Jurek Vaes, Urbain |
| author_facet | Gerber, Nicolai Jurek Vaes, Urbain |
| contents | This paper presents an elementary proof of quantitative uniform-in-time propagation of chaos for the Cucker--Smale model under sufficiently strong interaction. The idea is to combine existing finite-time propagation of chaos estimates with existing uniform-in-time stability estimates for the interacting particle system, in order to obtain a uniform-in-time propagation of chaos estimate with an explicit rate of convergence in the number of particles. This is achieved via a method that is similar in spirit to the classical 'stability + consistency implies convergence' approach in numerical analysis. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_15517 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Uniform-in-time propagation of chaos for the Cucker--Smale model Gerber, Nicolai Jurek Vaes, Urbain Probability Analysis of PDEs 34D05, 35Q70 (Primary) 34D06, 65M12 (Secondary) This paper presents an elementary proof of quantitative uniform-in-time propagation of chaos for the Cucker--Smale model under sufficiently strong interaction. The idea is to combine existing finite-time propagation of chaos estimates with existing uniform-in-time stability estimates for the interacting particle system, in order to obtain a uniform-in-time propagation of chaos estimate with an explicit rate of convergence in the number of particles. This is achieved via a method that is similar in spirit to the classical 'stability + consistency implies convergence' approach in numerical analysis. |
| title | Uniform-in-time propagation of chaos for the Cucker--Smale model |
| topic | Probability Analysis of PDEs 34D05, 35Q70 (Primary) 34D06, 65M12 (Secondary) |
| url | https://arxiv.org/abs/2501.15517 |