{
  "abstract": "Quantitative Gaussian approximation estimates on path space are established for the nonequilibrium density fluctuations of the simple symmetric exclusion process (SSEP) on a $d$-dimensional discrete torus of mesh size $1/n$, started from a product measure with a smooth density profile. A novel $n$-dependent modified Ornstein-Uhlenbeck process is constructed that incorporates higher-order lattice information while remaining linear and Gaussian. It is shown that, for sufficiently high modification orders, this modification yields quantitative Gaussian approximation error bounds of order $n^{-\\min\\{d/2,2\\}}$ for a class of smooth functionals of the entire fluctuation trajectory. In addition, it is shown that retaining an explicit microscopic correlation correction leaves a remainder of order $n^{-d/2}$, thereby distinguishing contributions to the bound due to correlations from those due to spatial approximation. For nonconstant initial profiles in dimensions $d\\ge3$, a separate argument yields matching upper and lower bounds of order $n^{-2}$ for the direct weak error of suitable quadratic test functionals, provided that the modification orders are sufficiently high. The proof is based on a novel path-dependent Trotter formula. Its derivation builds on the introduction of a concept of horizontal absolute continuity for non-anticipative functionals and a corresponding martingale formula for Markov jump processes. This formula is subsequently combined with an integral backward Kolmogorov equation for Gaussian continuation functionals. A second ingredient of the proof is a refinement of the exchangeable-pair argument introduced by the authors in a previous work, thereby improving the central-limit rate $n^{-\\min\\{d/2,1\\}}$ to $n^{-d/2}$ for the initial empirical fluctuations.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.13308",
  "author_total": 2,
  "authors": [
    {
      "name": "Benjamin Gess"
    },
    {
      "name": "Vitalii Konarovskyi"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/e4cghbb3kt4eb.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.13308",
  "fulltext_url": null,
  "id": "e4cghbb3kt4eb",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.13308",
  "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",
      "math.PR"
    ],
    [
      "openalex",
      "2610|Stochastic processes and statistical mechanics"
    ]
  ],
  "openalex": "W7221561523",
  "pdf_url": "https://arxiv.org/pdf/2610.13308",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-09",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/e4cghbb3kt4eb.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:28:40Z",
      "native_id": "2610.13308",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.13308"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Higher-Order Gaussian Approximations on Path Space for the Simple Symmetric Exclusion Process",
  "title_text": "Higher-Order Gaussian Approximations on Path Space for the Simple Symmetric Exclusion Process",
  "type": "preprint",
  "updated_at": "2026-10-30T12:28:40Z",
  "url": "https://research.draconitic.com/paper/e4cghbb3kt4eb",
  "venue": "arXiv",
  "versions": []
}