Quasi-stationarity of the Dyson Brownian motion with collisions

Arnaud Guillin, Boris Nectoux and Liming Wu

Stochastic Processes and their Applications, 2026, vol. 193, issue C

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. Cépa and D. Lépingle, 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.].

Keywords: Quasi-stationarity; Killed multivalued SDEs; Dyson Brownian motion (search for similar items in EconPapers)
Date: 2026
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DOI: 10.1016/j.spa.2025.104851

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