{
  "abstract": "We study the quenched pressure of the nearest-neighbor Edwards--Anderson Ising model with free and periodic boundary conditions. First, we prove that the infinite-volume pressure is $βd$-Lipschitz in the coupling law for the $1$-Wasserstein distance, yielding quantitative thermodynamic limits for spatially inhomogeneous disorder. Second, for periodic volumes, we prove that almost-sure convergence under every joint coupling of the finite-volume disorder arrays is equivalent to complete convergence of the one-volume pressure laws. Third, we prove that $\\mathbb{E}\\vert{}J\\vert{}^{1+1/d}<\\infty$ guarantees this universal-coupling conclusion. We further show that this exponent is optimal among uniform power-moment assumptions: for every $1\\leq q<1+1/d$, there is a centered symmetric law with finite $q$-th moment for which canonical nested volumes converge almost surely, whereas independently resampled volumes with the same fixed-volume marginals converge in probability but not almost surely. Finally, in dimension one, we prove that the first-moment condition is also necessary for a finite limiting pressure.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.09680",
  "author_total": 3,
  "authors": [
    {
      "name": "Mauris Chueng"
    },
    {
      "name": "Hexiang Wang"
    },
    {
      "name": "Keheng Zhu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/cpscsxx5ky4f8.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.09680",
  "fulltext_url": null,
  "id": "cpscsxx5ky4f8",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.09680",
  "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.dis-nn"
    ],
    [
      "arxiv",
      "math-ph"
    ],
    [
      "arxiv",
      "math.MP"
    ],
    [
      "arxiv",
      "math.PR"
    ],
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      "openalex",
      "2610|Stochastic processes and statistical mechanics"
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  "openalex": "W7212162148",
  "pdf_url": "https://arxiv.org/pdf/2609.09680",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-09",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/cpscsxx5ky4f8.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:20:12Z",
      "native_id": "2609.09680",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.09680"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    },
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.dis-nn",
      "subfield": "condensed-matter"
    }
  ],
  "title": "Wasserstein Stability, Couplings Across Volumes, and the $1+1/d$ Moment Thresholds in the Edwards--Anderson Model",
  "title_text": "Wasserstein Stability, Couplings Across Volumes, and the 1+1/d Moment Thresholds in the Edwards--Anderson Model",
  "type": "preprint",
  "updated_at": "2026-10-30T12:20:15Z",
  "url": "https://research.draconitic.com/paper/cpscsxx5ky4f8",
  "venue": "arXiv",
  "versions": []
}