Conditional GMC within the stochastic heat flow
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866909698466250752 |
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| author | Clark, Jeremy Tsai, Li-Cheng |
| author_facet | Clark, Jeremy Tsai, Li-Cheng |
| contents | We establish that the family of polymer measures $M^θ_{[s,t]}$ associated with the Stochastic Heat Flow (SHF), indexed by $θ\in\mathbb{R}$, has a conditional Gaussian Multiplicative Chaos (GMC) structure. Namely, taking the random measure $M^θ_{[s,t]}$ as the reference measure, we construct the path-space GMC with noise strength $a > 0$ and prove that the resulting random measure is equal in law to $M^{θ+a}_{[s,t]}$. As two applications, we prove that the polymer measure and SHF tested against general nonnegative functions are almost surely strictly positive and that the SHF converges to $0$ as $θ\to\infty$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_16056 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Conditional GMC within the stochastic heat flow Clark, Jeremy Tsai, Li-Cheng Probability We establish that the family of polymer measures $M^θ_{[s,t]}$ associated with the Stochastic Heat Flow (SHF), indexed by $θ\in\mathbb{R}$, has a conditional Gaussian Multiplicative Chaos (GMC) structure. Namely, taking the random measure $M^θ_{[s,t]}$ as the reference measure, we construct the path-space GMC with noise strength $a > 0$ and prove that the resulting random measure is equal in law to $M^{θ+a}_{[s,t]}$. As two applications, we prove that the polymer measure and SHF tested against general nonnegative functions are almost surely strictly positive and that the SHF converges to $0$ as $θ\to\infty$. |
| title | Conditional GMC within the stochastic heat flow |
| topic | Probability |
| url | https://arxiv.org/abs/2507.16056 |