Long-time propagation of chaos and exit times for metastable mean-field particle systems
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arXiv
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866915177634463744 |
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| author | Monmarché, Pierre |
| author_facet | Monmarché, Pierre |
| contents | Systems of stochastic particles evolving in a multi-well energy landscape and attracted to their barycenter is the prototypical example of mean-field process undergoing phase transitions: at low temperature, the corresponding mean-field deterministic limit has several stationary solutions, and the empirical measure of the particle system is then expected to be a metastable process in the space of probability measures, exhibiting rare transitions between the vicinity of these stationary solutions. We show two results in this direction: first, the exit time from such metastable domains occurs at time exponentially large with the number of particles and follows approximately an exponential distribution; second, up to the expected exit time, the joint law of particles remain close to the law of independent non-linear McKean-Vlasov processes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_00157 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Long-time propagation of chaos and exit times for metastable mean-field particle systems Monmarché, Pierre Probability Mathematical Physics Systems of stochastic particles evolving in a multi-well energy landscape and attracted to their barycenter is the prototypical example of mean-field process undergoing phase transitions: at low temperature, the corresponding mean-field deterministic limit has several stationary solutions, and the empirical measure of the particle system is then expected to be a metastable process in the space of probability measures, exhibiting rare transitions between the vicinity of these stationary solutions. We show two results in this direction: first, the exit time from such metastable domains occurs at time exponentially large with the number of particles and follows approximately an exponential distribution; second, up to the expected exit time, the joint law of particles remain close to the law of independent non-linear McKean-Vlasov processes. |
| title | Long-time propagation of chaos and exit times for metastable mean-field particle systems |
| topic | Probability Mathematical Physics |
| url | https://arxiv.org/abs/2503.00157 |