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arXiv · 2603.03246

Log Log Fluctuations of the Stochastic Heat Flow

Yu Gu·Li-Cheng Tsai
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Abstract

We study the stochastic heat flow with constant initial data and analyze its spatial average on the scale of $\varepsilon\ll1$. We prove that the logarithm of the averaged process satisfies a pointwise central limit theorem: After being centered by $-\tfrac{1}{2}\log\log \varepsilon^{-1}$ and scaled down by $\sqrt{\log\log \varepsilon^{-1}}$, it converges in distribution to a standard Gaussian.

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BibTeXRIS

Yu Gu, Li-Cheng Tsai. 2026-03-03. Log Log Fluctuations of the Stochastic Heat Flow. https://arxiv.org/abs/2603.03246

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