Breakthrough Tracker record

An AI-assisted preprint constructs a critical two-dimensional KPZ process

Berger, Caravenna, Clark and collaborators construct a non-Gaussian distribution-valued process as the critical limit of centred log partition functions for two-dimensional Gaussian directed polymers and as a renormalized Cole–Hopf functional of the critical stochastic heat flow.

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Stable ID: math-critical-two-dimensional-kpz-process-2026
Revision: math-critical-two-dimensional-kpz-process-2026.v1
Field: Mathematics and mathematical physics · Probability, stochastic partial differential equations and mathematical physics
Evidence: Tier 1 · Peer reviewed: No
Record state: Provisional · Provisional construction
Last checked: 2026-10-25

AI role

The eleven authors report extensive work with ChatGPT 5.5, 5.6 and 6. They attribute contributions to tightness, convergence to a unique limit and non-Gaussianity, describe discarded AI-generated approaches, and state that they checked and revised the arguments and take responsibility for the final manuscript.

Record details

Problem or result: Construction and characterization of a critical two-dimensional KPZ process
Authors: Quentin Berger, Francesco Caravenna, Jeremy Clark, Alexander Dunlap, Yu Gu, Ziyang Liu, Shuta Nakajima, Rongfeng Sun, Li-Cheng Tsai, Zuodi Xie and Nikos Zygouras
Institutions: Université Sorbonne Paris Nord; University of Milano-Bicocca; University of Mississippi; Duke University; University of Maryland; Hong Kong University of Science and Technology; Keio University; National University of Singapore; University of Utah; University of Warwick
Result date: First-version preprint submitted October 22, 2026

Why it matters

The two-dimensional KPZ equation is ill-defined at criticality without renormalization. The proposed process supplies a nontrivial critical object, connects it to the previously constructed stochastic heat flow and identifies non-Gaussian local behavior at the marginal dimension.

Limits

This is an 84-page unrefereed preprint and no independent specialist correctness assessment was located. The result is a mathematically constructed scaling limit, not an experimental demonstration or a claim that every two-dimensional KPZ model has been solved. Its extensive AI contribution makes author checking important but is not independent validation.

Sources

Primary: Berger and collaborators, The Critical 2D KPZ Process
Foundational context: Caravenna, Sun and Zygouras, The critical 2D stochastic heat flow

Correction and revision history

2026-10-25 — Added after primary-source, scope, status, AI-role and limitation review.

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