October 9, 2025Open Access

Stochastic heat flow is a black noise

Key Points

The research establishes that stochastic heat flow is a black noise, revealing significant properties of heat equations.
A critical finding shows that the 2D stochastic heat equation reacts differently with white noise, particularly in the scaling limit.
The proof relates back to established theories from Tsirelson and contemporaries, integrating foundational concepts from previous studies.
This study emphasizes the importance of understanding stochastic behaviors, which may have implications in advanced mathematical physics.

Abstract

We prove that the stochastic heat flow Caravenna Sun Zygouras (2023), Tsai (2024) is a black noise in the sense of Tsirelson (2004). As a corollary, the 2d stochastic heat equation driven by a mollified spacetime white noise becomes asymptotically independent of that noise in the scaling limit.

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Cite This Study

Gu et al. (Thu,) studied this question.

synapsesocial.com/papers/68e8439a9989581a2fd4e1b8 https://doi.org/https://doi.org/10.48550/arxiv.2506.16484

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