Zachary Adams (Concordia University)
CRM Applied Mathematics Seminars, Winter 2026
Title:Â Metastable clustering in weakly interacting particle systems
Abstract: We consider systems of N particles moving as Brownian motions and interacting via a bounded, locally attractive potential. In the large particle number limit, the empirical measure of such a system is known to converge to a nonlocal parabolic PDE of McKean-Vlasov type. While the McKean-Vlasov PDE corresponding to such systems is known to possess no non-trivial stationary solutions, numerical experiments demonstrate the existence of an almost-synchronized "cluster" state that persists over a long time scale. In this talk, we quantitatively characterize this cluster state and the time scale over which it persists using tools from spectral theory, thereby providing a partial answer to a question posed by Carrillo, Craig, and Yao (2019) in the microscopic setting. Time permitting, we will discuss the application of similar techniques to metastable states appearing in other systems. This is joint work with Maximilian Engel and Rishabh Gvalani.