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arXiv · 2504.08467

Quasi-stationarity of the Dyson Brownian motion with collisions

Arnaud Guillin·Boris Nectoux·Liming Wu
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Abstract

In this work, we investigate the ergodic behavior of a system of particules, subject to collisions, before it exits a fixed subdomain of its state space. This system is composed of several one-dimensional ordered Brownian particules in interaction with electrostatic repulsions, which is usually referred as the (generalized) Dyson Brownian motion. The starting points of our analysis are the work [E. C{\'e}pa and D. L{\'e}pingle, 1997 Probab. Theory Relat. Fields] which provides existence and uniqueness of such a system subject to collisions via the theory of multivalued SDEs and a Krein-Rutman type theorem derived in [A. Guillin, B. Nectoux, L. Wu, 2020 J. Eur. Math. Soc.].

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Arnaud Guillin, Boris Nectoux, Liming Wu. 2025-04-11. Quasi-stationarity of the Dyson Brownian motion with collisions. https://arxiv.org/abs/2504.08467

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