{
  "abstract": "This paper studies the clustering behaviour of weakly interacting diffusions under the influence of sufficiently localized attractive interaction potentials on the one-dimensional torus. We describe how this clustering behaviour 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. We analyse different timescales for the particle system and the mean-field (McKean–Vlasov) PDE, arguing that while the particle system can exhibit coarsening by both coalescence and diffusive mass exchange between clusters, the clusters in the mean-field PDE are unable to move and coarsening occurs via the mass exchange of clusters. By introducing a new model for this mass exchange, we argue that the PDE exhibits dynamical metastability. We conclude by presenting careful numerical experiments that demonstrate the validity of our model.",
  "abstract_shown": true,
  "affiliations": [
    "Ulm University",
    "University of Edinburgh",
    "EPFL",
    "Imperial College London"
  ],
  "article_type": null,
  "arxiv": null,
  "author_total": 5,
  "authors": [
    {
      "affs": [
        0
      ],
      "name": "Nicolai Jurek Gerber",
      "orcid": "0009-0009-6658-5367"
    },
    {
      "affs": [
        1
      ],
      "name": "Rishabh S. Gvalani",
      "orcid": "0000-0003-2078-3383"
    },
    {
      "affs": [
        2,
        3
      ],
      "name": "Martin Hairer",
      "orcid": "0000-0002-2141-6561"
    },
    {
      "affs": [
        3
      ],
      "name": "G A Pavliotis",
      "orcid": "0000-0002-3468-9227"
    },
    {
      "affs": [
        0
      ],
      "name": "André Schlichting",
      "orcid": "0000-0003-4140-491X"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/6ezqk0gwheat4.bib",
  "cited_by": 18,
  "doi": "10.1088/1361-6544/ae7ee7",
  "fulltext_url": null,
  "id": "6ezqk0gwheat4",
  "issns": [
    "0951-7715",
    "1361-6544"
  ],
  "landing_url": "https://doi.org/10.1088/1361-6544/ae7ee7",
  "language": "en",
  "licence": "CC-BY",
  "licence_label": "CC BY",
  "licence_source": "journal",
  "licence_url": "https://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": null,
  "native_subjects": [
    [
      "openalex",
      "2610|Stochastic processes and statistical mechanics"
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  "openalex": "W4415965543",
  "pdf_url": "https://iopscience.iop.org/article/10.1088/1361-6544/ae7ee7/pdf",
  "pmcid": null,
  "pmid": null,
  "published": "2026-07-23",
  "publisher": "IOP Publishing",
  "ris": "https://research.draconitic.com/paper/6ezqk0gwheat4.ris",
  "sources": [
    {
      "first_seen": "2026-11-07T13:20:41Z",
      "native_id": "W4415965543",
      "source": "openalex",
      "url": "https://doi.org/10.1088/1361-6544/ae7ee7"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "openalex:2610|Stochastic processes and statistical mechanics",
      "subfield": "mathematical-physics"
    }
  ],
  "title": "Formation of clusters and coarsening in weakly interacting diffusions",
  "title_text": "Formation of clusters and coarsening in weakly interacting diffusions",
  "type": "peer-reviewed",
  "updated_at": "2026-11-09T13:20:59Z",
  "url": "https://research.draconitic.com/paper/6ezqk0gwheat4",
  "venue": "Nonlinearity",
  "versions": []
}