Dyson Brownian motion on a Jordan curve
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866915837686841344 |
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| author | Guskov, Vladislav Liu, Mingchang Viklund, Fredrik |
| author_facet | Guskov, Vladislav Liu, Mingchang Viklund, Fredrik |
| contents | Zabrodin recently proposed a generalization of Dyson Brownian motion to a setting where the particles are confined to a smooth Jordan curve in the plane. In this paper, we discuss a rigorous construction of such a process on a rectifiable Jordan curve and study some of its basic properties. Under further smoothness assumptions, we derive the associated Fokker-Planck-Kolmogorov equation, prove convergence towards the stationary Coulomb gas distribution, study large deviations at low temperature, and derive the limiting mean-field McKean--Vlasov equation in the many-particle limit. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_05316 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Dyson Brownian motion on a Jordan curve Guskov, Vladislav Liu, Mingchang Viklund, Fredrik Probability Mathematical Physics Zabrodin recently proposed a generalization of Dyson Brownian motion to a setting where the particles are confined to a smooth Jordan curve in the plane. In this paper, we discuss a rigorous construction of such a process on a rectifiable Jordan curve and study some of its basic properties. Under further smoothness assumptions, we derive the associated Fokker-Planck-Kolmogorov equation, prove convergence towards the stationary Coulomb gas distribution, study large deviations at low temperature, and derive the limiting mean-field McKean--Vlasov equation in the many-particle limit. |
| title | Dyson Brownian motion on a Jordan curve |
| topic | Probability Mathematical Physics |
| url | https://arxiv.org/abs/2603.05316 |