{
  "abstract": "This work constructs a non-trivial solution to the ill-defined two-dimensional Kardar-Parisi-Zhang (KPZ) equation at criticality: a distribution-valued stochastic process on the plane, which we call the Critical 2D KPZ Process. It arises as the limit in law of centred log partition functions of two-dimensional Gaussian directed polymers at criticality, viewed as discretised KPZ solutions. It is also a measurable function of the Critical 2D Stochastic Heat Flow (SHF) via a renormalised Cole-Hopf transformation, obtained as the limit of the centred logarithm of the spatially mollified SHF as the smoothing is removed. The Critical 2D KPZ process is non-Gaussian and its covariance displays a log-log blow-up near the diagonal. Gaussian fluctuations emerge when averaging on shrinking spatial scales. The results presented here were obtained through extensive interactions with generative AI (ChatGPT 5.5, 5.6 and 6); see Appendix C for more details. The proof builds on key recent and older advances in our field, combined in novel ways with substantial AI input. We view this manuscript as a \"community project\" that represents more than a decade's collective effort. We have worked on making the presentation as accessible as possible, highlighting the main ideas and their relations to the literature.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.31614",
  "author_total": 11,
  "authors": [
    {
      "name": "Quentin Berger"
    },
    {
      "name": "Francesco Caravenna"
    },
    {
      "name": "Jeremy Clark"
    },
    {
      "name": "Alexander Dunlap"
    },
    {
      "name": "Yu Gu"
    },
    {
      "name": "Ziyang Liu"
    },
    {
      "name": "Shuta Nakajima"
    },
    {
      "name": "Rongfeng Sun"
    },
    {
      "name": "Li-Cheng Tsai"
    },
    {
      "name": "Zuodi Xie"
    },
    {
      "name": "Nikos Zygouras"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/63qydp0fjwfxy.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.31614",
  "fulltext_url": null,
  "id": "63qydp0fjwfxy",
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  "landing_url": "https://arxiv.org/abs/2610.31614",
  "language": "en",
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  "metadata_licence": "CC0-1.0",
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      "2610|Stochastic processes and statistical mechanics"
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  "pdf_url": "https://arxiv.org/pdf/2610.31614",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-22",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/63qydp0fjwfxy.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:34Z",
      "native_id": "2610.31614",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.31614"
    },
    {
      "first_seen": "2026-11-02T12:20:44Z",
      "native_id": "hal-05847240",
      "source": "hal",
      "url": "https://hal.science/hal-05847240v1"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "The Critical 2D KPZ Process",
  "title_text": "The Critical 2D KPZ Process",
  "type": "preprint",
  "updated_at": "2026-11-03T12:20:17Z",
  "url": "https://research.draconitic.com/paper/63qydp0fjwfxy",
  "venue": "arXiv",
  "versions": []
}