On uniform in time propagation of chaos in metastable cases: the Curie-Weiss model
Fuente:
arXiv
Guardado en:
| Autores principales: | , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2025
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866915144660942848 |
|---|---|
| author | Journel, Lucas Bris, Pierre Le |
| author_facet | Journel, Lucas Bris, Pierre Le |
| contents | Many low temperature particle systems in mean-field interaction are ergodic with respect to a unique invariant measure, while their (non-linear) mean-field limit may possess several steady states. In particular, in such cases, propagation of chaos (i.e. the convergence of the particle system to its mean-field limit as n, the number of particles, goes to infinity) cannot hold uniformly in time since the long-time behaviors of the two processes are a priori incompatible. However, the particle system may be metastable, and the time needed to exit the basin of attraction of one of the steady states of its limit, and go to another, is exponentially (in n) long. Before this exit time, the particle system reaches a (quasi-)stationary distribution, which we expect to be a good approximation of the corresponding non-linear steady state. Our goal is to study the typical metastable behavior of the empirical measure of such mean-field systems, starting in this work with the Curie-Weiss model. We thus show uniform in time propagation of chaos of the spin system conditioned to keeping a positive magnetization. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_06429 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On uniform in time propagation of chaos in metastable cases: the Curie-Weiss model Journel, Lucas Bris, Pierre Le Probability Many low temperature particle systems in mean-field interaction are ergodic with respect to a unique invariant measure, while their (non-linear) mean-field limit may possess several steady states. In particular, in such cases, propagation of chaos (i.e. the convergence of the particle system to its mean-field limit as n, the number of particles, goes to infinity) cannot hold uniformly in time since the long-time behaviors of the two processes are a priori incompatible. However, the particle system may be metastable, and the time needed to exit the basin of attraction of one of the steady states of its limit, and go to another, is exponentially (in n) long. Before this exit time, the particle system reaches a (quasi-)stationary distribution, which we expect to be a good approximation of the corresponding non-linear steady state. Our goal is to study the typical metastable behavior of the empirical measure of such mean-field systems, starting in this work with the Curie-Weiss model. We thus show uniform in time propagation of chaos of the spin system conditioned to keeping a positive magnetization. |
| title | On uniform in time propagation of chaos in metastable cases: the Curie-Weiss model |
| topic | Probability |
| url | https://arxiv.org/abs/2502.06429 |