第140回

日時 Time

2026年3月30日（月）10:00–11:30

場所 Place

自然科学５号館研究棟2階 223室
Natural Science and Technology Hall 5, 2nd floor, Room 223

講演者 Speaker

Jasper Hoeksema (Eindhoven University of Technology)

タイトル Title

Condensation via Gamma-convergence and relaxation

概要 Abstract

Coagulation–fragmentation models describe how particles in large interacting systems can form clusters that subsequently break apart. When formulated as an infinite system of ordinary differential equations, these dynamics can exhibit instability and loss of well-posedness. This behaviour is closely related to the phenomenon of condensation: the emergence of a macroscopic cluster that exchanges mass with all finite clusters.
In this talk, we analyse the many-particle limit of such systems via Gamma-convergence of associated Lyapunov functionals, which characterise equilibrium statistics. We show that condensation arises from a relaxation phenomenon, where integral functionals subject to constraints that are not continuous in the relevant topology acquire additional singular terms in the limit. These terms encode the condensed phase and explain the apparent interaction between finite clusters and the macroscopic one.
The talk is based on past and ongoing work with André Schlichting and Chun Yin Lam (Ulm University).