Multi-species McKean-Vlasov dynamics in non-convex landscapes
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866915381780676608 |
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| author | Duong, Manh Hong Pavliotis, Grigorios A. Tugaut, Julian |
| author_facet | Duong, Manh Hong Pavliotis, Grigorios A. Tugaut, Julian |
| contents | In this paper, we study multi-species stochastic interacting particle systems and their mean-field McKean-Vlasov partial differential equations (PDEs) in non-convex landscapes. We discuss the well-posedness of the multi-species SDE system, propagation of chaos and the derivation of the coupled McKean-Vlasov PDE system in the mean field limit. Our focus is on the long-time and asymptotic behaviour of the mean-field PDEs. Under suitable growth assumptions on the potentials and an appropriate structural assumption, we show the existence and (non-) uniqueness of stationary solutions and study their linear stability. Under a symmetry assumption we construct a free-energy functional that plays the role of a Lyapunov function for the mean-field PDE system. Furthermore, we prove the existence of a phase transition at low noise strengths and establish the convergence of solutions to the mean-field PDEs (and of their free energy) to a stationary state (and the corresponding free energy). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_07617 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Multi-species McKean-Vlasov dynamics in non-convex landscapes Duong, Manh Hong Pavliotis, Grigorios A. Tugaut, Julian Probability Mathematical Physics Analysis of PDEs In this paper, we study multi-species stochastic interacting particle systems and their mean-field McKean-Vlasov partial differential equations (PDEs) in non-convex landscapes. We discuss the well-posedness of the multi-species SDE system, propagation of chaos and the derivation of the coupled McKean-Vlasov PDE system in the mean field limit. Our focus is on the long-time and asymptotic behaviour of the mean-field PDEs. Under suitable growth assumptions on the potentials and an appropriate structural assumption, we show the existence and (non-) uniqueness of stationary solutions and study their linear stability. Under a symmetry assumption we construct a free-energy functional that plays the role of a Lyapunov function for the mean-field PDE system. Furthermore, we prove the existence of a phase transition at low noise strengths and establish the convergence of solutions to the mean-field PDEs (and of their free energy) to a stationary state (and the corresponding free energy). |
| title | Multi-species McKean-Vlasov dynamics in non-convex landscapes |
| topic | Probability Mathematical Physics Analysis of PDEs |
| url | https://arxiv.org/abs/2507.07617 |