2025/04/11 by Arnaud Guillin, Guillin, Arnaud, Boris Nectoux +3
Mathematics · #Data Analysis #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Probability (math.PR) #Random Matrices and Applications #Statistics and Probability (physics.data-an) #Stochastic processes and statistical mechanics
paper · pdf · doi:10.48550/arxiv.2504.08467
openalex publication_date 2025/04/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.].