Mean-field limits à la Tanaka and large deviations for particle systems with network interactions
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866915535084584960 |
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| author | Chaintron, Louis-Pierre Diez, Antoine |
| author_facet | Chaintron, Louis-Pierre Diez, Antoine |
| contents | This article proposes a unified framework to study non-exchangeable mean-field particle systems with some general interaction mechanisms. The starting point is a fixed-point formulation of particle systems originally due to Tanaka that allows us to prove mean-field limit and large deviation results in an abstract setting. While it has been recently shown that such formulation encompasses a large class of exchangeable particle systems, we propose here a setting for the non-exchangeable case, including the case of adaptive interaction networks. We introduce sufficient conditions on the network structure that imply the mean-field limit and a new large deviations principle for the interaction measure. Finally, we formally highlight important models for which it is possible to derive a closed PDE characterization of the limit. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_04894 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Mean-field limits à la Tanaka and large deviations for particle systems with network interactions Chaintron, Louis-Pierre Diez, Antoine Probability Analysis of PDEs 35Q70, 82C22, 82C31, 60H10, 60H30, 60F10, 05C80 This article proposes a unified framework to study non-exchangeable mean-field particle systems with some general interaction mechanisms. The starting point is a fixed-point formulation of particle systems originally due to Tanaka that allows us to prove mean-field limit and large deviation results in an abstract setting. While it has been recently shown that such formulation encompasses a large class of exchangeable particle systems, we propose here a setting for the non-exchangeable case, including the case of adaptive interaction networks. We introduce sufficient conditions on the network structure that imply the mean-field limit and a new large deviations principle for the interaction measure. Finally, we formally highlight important models for which it is possible to derive a closed PDE characterization of the limit. |
| title | Mean-field limits à la Tanaka and large deviations for particle systems with network interactions |
| topic | Probability Analysis of PDEs 35Q70, 82C22, 82C31, 60H10, 60H30, 60F10, 05C80 |
| url | https://arxiv.org/abs/2510.04894 |