Preprint: Formation of clusters and coarsening in weakly interacting diffusions
Together with Nicolai Gerber, Rishabh Gvalani, Martin Hairer and Greg Pavliotis, we study the clustering behavior of weakly interacting diffusions under the influence of sufficiently localized attractive interaction potentials on the one-dimensional torus. We describe how this clustering behavior is closely related to the presence of discontinuous phase transitions in the mean-field PDE. For local attractive interactions, we employ a new variant of the strict Riesz rearrangement inequality to prove that all global minimizers of the free energy are either uniform or single-cluster states, in the sense that they are symmetrically decreasing.
Now published in Nonlinearity 39(7), 075023 (2026).
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