{
  "abstract": "We prove a canonical (or fixed-population) local equilibrium theorem for the symmetric simple exclusion process on the discrete torus $\\mathbb T_N^D$, $D\\ge2$, at particle densities bounded away from $0$ and $1$, uniformly over all deterministic initial configurations with the prescribed particle number. At times \\[ t_N(s)=\\frac{\\log(N^D)+s}{2γ_N}, \\qquad γ_N=2-2\\cos\\left(\\frac{2π}{N}\\right), \\] the Radon--Nikodym density of the process relative to equilibrium converges in $L^2$ to a canonical exponential tilt generated by the unique small mean-zero calibration field whose one-site marginals match the evolving one-particle heat profile. Consequently, whenever the profile coordinate converges, the corresponding total variation profile is a Gaussian shift. More precisely, for a deterministic initial sequence $(S_N)$, if the covariance-normalized squared amplitude $\\mathfrak q_N^{S_N}(s)$ converges to a scalar $\\mathfrak q$ at a fixed $s$, then the distance to stationarity converges to $ 2Φ\\!\\left({\\sqrt{\\mathfrak q}}/2\\right)-1 $, where $Φ$ is the standard normal distribution function. The profile coordinate is asymptotically determined by the one-particle eigenspace corresponding to the smallest nonzero eigenvalue. The proof combines a calibrated canonical comparison, a fixed-degree comparison between independent and exclusion dynamics, and all-degree control obtained from pair energy estimates and preservation of the Strong--Rayleigh property.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.10304",
  "author_total": 1,
  "authors": [
    {
      "name": "Joe P. Chen"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/fa04hqz0bf33z.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.10304",
  "fulltext_url": null,
  "id": "fa04hqz0bf33z",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.10304",
  "language": null,
  "licence": "CC-BY-SA-4.0",
  "licence_label": "CC BY-SA 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-sa/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math-ph"
    ],
    [
      "arxiv",
      "math.MP"
    ],
    [
      "arxiv",
      "math.PR"
    ],
    [
      "openalex",
      "2610|Stochastic processes and statistical mechanics"
    ]
  ],
  "openalex": "W7212132186",
  "pdf_url": "https://arxiv.org/pdf/2609.10304",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-09",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/fa04hqz0bf33z.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:20:12Z",
      "native_id": "2609.10304",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.10304"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Canonical Local Equilibrium and Cutoff Profiles for the Symmetric Exclusion Process on Discrete Tori",
  "title_text": "Canonical Local Equilibrium and Cutoff Profiles for the Symmetric Exclusion Process on Discrete Tori",
  "type": "preprint",
  "updated_at": "2026-10-30T12:20:15Z",
  "url": "https://research.draconitic.com/paper/fa04hqz0bf33z",
  "venue": "arXiv",
  "versions": []
}