{
  "abstract": "For a large class of discrete- and continuous-time models satisfying a linear flow property, we prove convergence to the critical $2d$ stochastic heat flow under diffusive scaling of space and time. Convergence is in the sense of finite-dimensional distributions in the space of measure-valued stochastic flows. The class of discrete models we consider includes random walks in space-time random environments with finite-range jumps, and directed polymer models with finite-range spatial correlations. The class of continuum models we consider includes several distinct types of linear-multiplicative stochastic PDEs whose driving noise is Gaussian with a smooth and compactly supported covariance kernel.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.15832",
  "author_total": 3,
  "authors": [
    {
      "name": "Hindy Drillick"
    },
    {
      "name": "Jonathan Hou"
    },
    {
      "name": "Shalin Parekh"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/dxw7nf68zvyhs.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.15832",
  "fulltext_url": null,
  "id": "dxw7nf68zvyhs",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.15832",
  "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.PR"
    ],
    [
      "openalex",
      "2610|Stochastic processes and statistical mechanics"
    ]
  ],
  "openalex": "W7213230254",
  "pdf_url": "https://arxiv.org/pdf/2609.15832",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-14",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/dxw7nf68zvyhs.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:21:29Z",
      "native_id": "2609.15832",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.15832"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "A universality result for the critical 2d stochastic heat flow",
  "title_text": "A universality result for the critical 2d stochastic heat flow",
  "type": "preprint",
  "updated_at": "2026-10-30T12:21:29Z",
  "url": "https://research.draconitic.com/paper/dxw7nf68zvyhs",
  "venue": "arXiv",
  "versions": []
}