{
  "abstract": "This is the third in a series of three papers in which we study a lattice gas subject to Kawasaki dynamics at inverse temperature β > 0 in a large finite box Λ β ⊂ Z 2 whose volume depends on β . Each pair of neighbouring particles has a negative binding energy − U < 0 , while each particle has a positive activation energy Δ > 0. The initial configuration is drawn from the grand-canonical ensemble restricted to the set of configurations where all the droplets are subcritical. Our goal is to describe, in the metastable regime Δ ∈ ( U , 2 U ) and in the limit as β → ∞, how and when the system nucleates, i.e., creates a critical droplet somewhere in Λ β that subsequently grows by absorbing particles from the surrounding gas. In the first paper we showed that subcritical droplets behave as quasi-random walks. In the second paper we used the results in the first paper to analyse how subcritical droplets form and dissolve on multiple space-time scales when the volume is moderately large , namely, | Λ β | = e Θ β with Δ < Θ < 2 Δ − U . In the present paper we consider the setting where the volume is very large , namely, | Λ β | = e Θ β with Θ < Γ − ( 2 Δ − U ) , where Γ is the energy of the critical droplet in the local model with fixed volume, and we use the results in the first two papers to identify the nucleation time and the tube of typical trajectories towards nucleation. We will see that in very large volumes critical droplets appear more or less independently in boxes of moderate volume, a phenomenon referred to as homogeneous nucleation . This leads to a nucleation time of order e Γ β /|Λ β |. One of the key ingredients in the proof is an estimate showing that no information can travel between the moderately large boxes on relevant time scales. Prior to nucleation, the dynamics inside the moderately large boxes spends most of its time in configurations consisting of a single quasi-square surrounded by free particles, and makes transitions between these configurations at rates that depend on the linear sizes of the quasi-square in a computable manner.",
  "abstract_shown": true,
  "affiliations": [
    "Gran Sasso Science Institute, Viale Francesco Crispi 7, 67100, L’Aquila, Italy",
    "Universiteit Leiden = Leiden University (Leiden University | 2300 RA Leiden The Netherlands - Netherlands)",
    "Aix-Marseille Université, CNRS, I2M, 3 Place Victor Hugo, 13003, Marseille, France",
    "I2M - Institut de Mathématiques de Marseille (Centre de Mathématiques et Informatique (CMI) Technopôle Château-Gombert 39, rue Frédéric Joliot Curie 13453 Marseille Cedex 13 - France)",
    "Mathematisch Instituut, Universiteit Leiden, Einsteinweg 55, 2333 CC, Leiden, The Netherlands",
    "Università degli Studi di Firenze, Dipartimento di Matematica e Informatica “Ulisse Dini”, Viale Morgagni 67/a, 50134, Firenze, Italy",
    "Dipartimento di Matematica , Università di Roma Tor Vergata , Via della Ricerca Scientifica , Roma , 00133 , Italy",
    "Dipartimento di Matematica e Fisica, Universit‘a di Roma Tre, Largo S. Leonardo Murialdo 1, 00146, Roma, Italy"
  ],
  "article_type": null,
  "arxiv": null,
  "author_total": 6,
  "authors": [
    {
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        0,
        1
      ],
      "name": "Simone Baldassarri",
      "orcid": "0000-0001-9548-6370"
    },
    {
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        2,
        3
      ],
      "name": "Alexandre Gaudillière",
      "orcid": "0000-0002-1507-5721"
    },
    {
      "affs": [
        4,
        1
      ],
      "name": "Frank den Hollander",
      "orcid": "0000-0003-2866-9470"
    },
    {
      "affs": [
        5
      ],
      "name": "Francesca Romana Nardi",
      "orcid": "0000-0001-9887-2592"
    },
    {
      "affs": [
        6
      ],
      "name": "Enzo Olivieri",
      "orcid": "0000-0002-9968-2245"
    },
    {
      "affs": [
        7
      ],
      "name": "Elisabetta Scoppola",
      "orcid": "0000-0002-4495-0310"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/dzk9nxh0n0ys3.bib",
  "cited_by": 5,
  "doi": "10.1016/j.spa.2026.105031",
  "fulltext_url": null,
  "id": "dzk9nxh0n0ys3",
  "issns": [
    "0304-4149",
    "1879-209X"
  ],
  "landing_url": "https://doi.org/10.1016/j.spa.2026.105031",
  "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": [
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      "openalex",
      "2610|Stochastic processes and statistical mechanics"
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  "openalex": "W4399416868",
  "pdf_url": "https://www.sciencedirect.com/science/article/pii/S0304414926001638/pdf",
  "pmcid": null,
  "pmid": null,
  "published": "2026-06-24",
  "publisher": "Elsevier BV",
  "ris": "https://research.draconitic.com/paper/dzk9nxh0n0ys3.ris",
  "sources": [
    {
      "first_seen": "2026-11-04T13:21:00Z",
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      "url": "https://doi.org/10.1016/j.spa.2026.105031"
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  "subjects": [
    {
      "field": "mathematics",
      "origin": "openalex:2610|Stochastic processes and statistical mechanics",
      "subfield": "mathematical-physics"
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  ],
  "title": "Homogeneous nucleation for two-dimensional Kawasaki dynamics",
  "title_text": "Homogeneous nucleation for two-dimensional Kawasaki dynamics",
  "type": "peer-reviewed",
  "updated_at": "2026-11-04T13:21:00Z",
  "url": "https://research.draconitic.com/paper/dzk9nxh0n0ys3",
  "venue": "Stochastic Processes and their Applications",
  "versions": []
}