{
  "abstract": "We consider the Asymmetric Simple Exclusion Process (ASEP) at its critical dimension $d=2$, started from the Bernoulli product measure with density $ρ\\in (0,1)$. We first derive the sharp $\\log(t)^{2/3}$ divergence of the bulk diffusivity, predicted via mode-coupling theory in [H. van Beijeren, R. Kutner, H. Spohn, Phys. Rev. Lett., 1985], including the exact prefactor, thereby removing the subleading diverging multiplicative corrections in the Tauberian bounds of [H.-T. Yau, Ann. of Math., 2004]. More importantly, we establish an invariance principle for the density fluctuation field on the corresponding superdiffusive scales. On the time scale $τ$, we rescale space by $\\sqrtτ \\log(τ)^{1/3}$ in the direction of the drift and by $\\sqrtτ$ in the transverse direction, and prove functional convergence of the rescaled fluctuation process to the solution of a conservative stochastic heat equation with additive noise. This is the same explicit Gaussian Fixed Point obtained in [G. Cannizzaro, Q. Moulard, F. Toninelli, arXiv:2501.00344, 2025] for the two-dimensional Stochastic Burgers Equation (SBE). We also deduce a superdiffusive central limit theorem for the second-class particle under the same anisotropic rescaling. The result holds for any finite-range jump kernel with nonzero drift and uniaxial asymmetry. This is the first space-time scaling limit result for a nonequilibrium interacting particle system at the critical dimension, where Gaussian fluctuations emerge despite logarithmic corrections to the scaling. The proof uses an approximate fluctuation-dissipation relation, which is obtained by combining a sharp quantitative comparison between the ASEP and SBE generators with refined estimates on the SBE Ansatz. An additional key novelty is a tightness argument that overcomes the limitations of the Itô trick on superdiffusive scales.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.18847",
  "author_total": 1,
  "authors": [
    {
      "name": "Quentin Moulard"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/67cagbekw7m9s.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.18847",
  "fulltext_url": null,
  "id": "67cagbekw7m9s",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.18847",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/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": "W7221760829",
  "pdf_url": "https://arxiv.org/pdf/2610.18847",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-13",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/67cagbekw7m9s.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:11Z",
      "native_id": "2610.18847",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.18847"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Superdiffusive Invariance Principle for the two-dimensional Asymmetric Simple Exclusion Process",
  "title_text": "Superdiffusive Invariance Principle for the two-dimensional Asymmetric Simple Exclusion Process",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:20Z",
  "url": "https://research.draconitic.com/paper/67cagbekw7m9s",
  "venue": "arXiv",
  "versions": []
}