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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Materias: | |
| Acceso en línea: | https://arxiv.org/abs/2507.16056 |
| Etiquetas: |
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- 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 $θ\to\infty$.