Let the two-dimensional critical stochastic heat flow be the flow of random measures on R^2 constructed as the scaling limit of intermediate-disorder directed-polymer partition functions. Two-dimensional critical stochastic heat flow black-noise conjecture. The two-dimensional critical stochastic heat flow is a black noise. The conjecture concerns whether this recently constructed two-dimensional random field has no nonzero linear random variables in the sense of black-noise theory; the source gives no resolution.

Two-dimensional critical stochastic heat flow black-noise conjecture

The conjecture says that the two-dimensional critical stochastic heat flow has no nonzero linear random variables, making it a black noise. It arose from the scaling-limit construction of critical directed polymers and was explicitly stated in 2024.

Known results

The critical two-dimensional stochastic heat flow was constructed as a universal scaling limit of directed-polymer partition functions in 2021.
The 2024 formulation notes that the conjecture would imply a decoupling theorem for two-dimensional polymers.

June 2025 claimed proof

A June 2025 arXiv paper, “Stochastic Heat Flow is a Black Noise,” claims the exact result, asserting that the first chaos is trivial. A July 2025 paper proves independence between the critical stochastic heat flow and limiting white noise, but does not itself claim the black-noise theorem.

Current status (as of September 2026): A June 2025 preprint claims to settle the conjecture, while the supplied record contains no independent verification; absent acceptance of that claim, the conjecture remains formally unresolved.

Two-dimensional critical stochastic heat flow black-noise conjecture

Primary source

Progress summary

Solutions 0