Dyson Brownian motion on a Jordan curve
Probability
2026-03-06 v1 Mathematical Physics
math.MP
Abstract
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.
Keywords
Cite
@article{arxiv.2603.05316,
title = {Dyson Brownian motion on a Jordan curve},
author = {Vladislav Guskov and Mingchang Liu and Fredrik Viklund},
journal= {arXiv preprint arXiv:2603.05316},
year = {2026}
}