{
  "abstract": "We study the fixed-particle limit of empirical measures for a unified self-dual family of conservative particle systems on $\\mathbb{Z}^d$: independent random walkers, the symmetric exclusion process, and the symmetric inclusion process. For a fixed number of particles $k$, under diffusive space-time scaling parametrised by $n$, we prove that as $n\\to\\infty$ the normalised empirical measure converges in $D([0,T],\\mathcal{M}_1(\\mathbb{R}^d))$ to an atomic empirical measure carried by $k$ independent diffusions, with constant covariance determined by the microscopic jump kernel. Equivalently, the limit is the unique atomic solution of the Dean-Kawasaki martingale problem with mass quantisation $1/k$. In particular, exclusion and inclusion have the same fixed-$k$ atomic limit as independent walkers: the interaction contributes only through microscopic near-collisions, whose rescaled occupation time vanishes. The proof combines self-duality, consistency-based reduction to two particles, and Green-function estimates for finite perturbations of symmetric random walks.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.31319",
  "author_total": 3,
  "authors": [
    {
      "name": "Mario Ayala"
    },
    {
      "name": "Nicolas Dirr"
    },
    {
      "name": "Johannes Zimmer"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/5w933e27m69z2.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.31319",
  "fulltext_url": null,
  "id": "5w933e27m69z2",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.31319",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cond-mat.stat-mech"
    ],
    [
      "arxiv",
      "math-ph"
    ],
    [
      "arxiv",
      "math.MP"
    ],
    [
      "arxiv",
      "math.PR"
    ],
    [
      "openalex",
      "2610|Stochastic processes and statistical mechanics"
    ]
  ],
  "openalex": "W7223380974",
  "pdf_url": "https://arxiv.org/pdf/2610.31319",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-22",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/5w933e27m69z2.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:34Z",
      "native_id": "2610.31319",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.31319"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    },
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.stat-mech",
      "subfield": "statistical-nonlinear"
    }
  ],
  "title": "Atomic limits of empirical measures of interacting particle systems with self-duality",
  "title_text": "Atomic limits of empirical measures of interacting particle systems with self-duality",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:38Z",
  "url": "https://research.draconitic.com/paper/5w933e27m69z2",
  "venue": "arXiv",
  "versions": []
}