Formation of clusters and coarsening in weakly interacting diffusions

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**This talk will be broadcast at 13:30 BT / 14:30 CET / 15:30 EET, February 25th, 2026 on Zoom only. **

Meeting-ID: 667 4776 1513 Passcode: 834059

Abstract

How do weakly interacting diffusions on the one-dimensional torus behave under finite-range attractive interactions? In this talk, we explore different effects, such as cluster formation, and how clusters coarsen into single-cluster states. Depending on the parameter regime, this coarsening can occur through two distinct mechanisms: 1. Coalescence, where clusters move and merge like coalescing Brownian motions. 2. Mass exchange: Individual particles detach from one cluster and attach to another, enabling mass transfer between clusters. Based on a version of the Eyring-Kramers law, we introduce a joint model to describe these effects and argue that the corresponding deterministic mean-field PDE exhibits dynamical metastability through the mass exchange.

Moreover, we introduce a new variant of the strict Riesz rearrangement to characterize the global minimizers of the free energy, showing that they are either uniform or single-cluster states, i.e., symmetrically decreasing.

Joint work with R. Gvalani, M. Hairer, G. Pavliotis, and A. Schlichting.

About Nicolai

Nicolai is currently working on his PhD under the supervision of André Schlichting at the University of Ulm (Germany). He completed his master’s thesis with Franca Hoffmann at the University of Bonn. His research focuses on interacting particle systems, studying metastability, propagation of chaos, and coarsening.