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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2603.03246 |
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| _version_ | 1866908863262883840 |
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| author | Gu, Yu Tsai, Li-Cheng |
| author_facet | Gu, Yu Tsai, Li-Cheng |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_03246 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Log Log Fluctuations of the Stochastic Heat Flow Gu, Yu Tsai, Li-Cheng Probability 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. |
| title | Log Log Fluctuations of the Stochastic Heat Flow |
| topic | Probability |
| url | https://arxiv.org/abs/2603.03246 |