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| Natura: | Preprint |
| Pubblicazione: |
2024
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| Accesso online: | https://arxiv.org/abs/2412.14512 |
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| _version_ | 1866909548854378496 |
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| author | Zhou, Datong |
| author_facet | Zhou, Datong |
| contents | We study a non-exchangeable multi-agent system and rigorously derive a strong form of the mean-field limit. The convergence of the connection weights and the initial data implies convergence of large-scale dynamics toward a deterministic limit given by the corresponding extended Vlasov PDE, at any later time and any realization of randomness. This is established on what we call a bi-coupling distance defined through a convex optimization problem, which is an interpolation of the optimal transport between measures and the fractional overlay between graphs. The proof relies on a quantitative stability estimate of the so-called observables, which are tensorizations of agent laws and graph homomorphism densities. This reveals a profound relationship between mean-field theory and graph limiting theory, intersecting in the study of non-exchangeable systems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_14512 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Coupling and Tensorization of Kinetic Theory and Graph Theory Zhou, Datong Analysis of PDEs Combinatorics Probability 35Q70, 35Q83, 35R02, 05C90, 05C60, 05C22 We study a non-exchangeable multi-agent system and rigorously derive a strong form of the mean-field limit. The convergence of the connection weights and the initial data implies convergence of large-scale dynamics toward a deterministic limit given by the corresponding extended Vlasov PDE, at any later time and any realization of randomness. This is established on what we call a bi-coupling distance defined through a convex optimization problem, which is an interpolation of the optimal transport between measures and the fractional overlay between graphs. The proof relies on a quantitative stability estimate of the so-called observables, which are tensorizations of agent laws and graph homomorphism densities. This reveals a profound relationship between mean-field theory and graph limiting theory, intersecting in the study of non-exchangeable systems. |
| title | Coupling and Tensorization of Kinetic Theory and Graph Theory |
| topic | Analysis of PDEs Combinatorics Probability 35Q70, 35Q83, 35R02, 05C90, 05C60, 05C22 |
| url | https://arxiv.org/abs/2412.14512 |