A law of large numbers for kinetic interacting diffusions
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866912702922752000 |
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| author | Bellingeri, Carlo Coppini, Fabio |
| author_facet | Bellingeri, Carlo Coppini, Fabio |
| contents | We study the convergence of the empirical distribution associated with a system of interacting kinetic particles subject to independent Brownian forcing in a finite horizon setting, using some recent progress on kinetic non-linear partial differential equations. Under general assumptions that require only weak convergence on the initial datum -- without assuming independence or moment conditions -- we prove convergence in probability to the corresponding non-linear Fokker-Planck PDE. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_01769 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A law of large numbers for kinetic interacting diffusions Bellingeri, Carlo Coppini, Fabio Probability 60K35, 60F05, 60H20 We study the convergence of the empirical distribution associated with a system of interacting kinetic particles subject to independent Brownian forcing in a finite horizon setting, using some recent progress on kinetic non-linear partial differential equations. Under general assumptions that require only weak convergence on the initial datum -- without assuming independence or moment conditions -- we prove convergence in probability to the corresponding non-linear Fokker-Planck PDE. |
| title | A law of large numbers for kinetic interacting diffusions |
| topic | Probability 60K35, 60F05, 60H20 |
| url | https://arxiv.org/abs/2506.01769 |