Stochastic heat flow by moments
Fuente:
arXiv
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866915866040336384 |
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| author | Tsai, Li-Cheng |
| author_facet | Tsai, Li-Cheng |
| contents | The Stochastic Heat Flow (SHF) emerges as the scaling limit of directed polymers in random environments and the noise-mollified Stochastic Heat Equation (SHE), specifically at the critical dimension of two and near the critical temperature. The prior work Caravenna Sun Zygouras (2023) established the first construction of finite-dimensional distributions by demonstrating the universal (model-independent) convergence of discrete polymers. In this work, we present a new, independent approach to the SHF. We formulate the SHF as a continuous process and provide a set of axioms for its characterization. We establish both the uniqueness and existence of this process under our new formulation, with a key feature of these axioms being the matching of the first four moments. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_14657 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Stochastic heat flow by moments Tsai, Li-Cheng Probability 82C27 (Primary) 60H17 (Secondary) The Stochastic Heat Flow (SHF) emerges as the scaling limit of directed polymers in random environments and the noise-mollified Stochastic Heat Equation (SHE), specifically at the critical dimension of two and near the critical temperature. The prior work Caravenna Sun Zygouras (2023) established the first construction of finite-dimensional distributions by demonstrating the universal (model-independent) convergence of discrete polymers. In this work, we present a new, independent approach to the SHF. We formulate the SHF as a continuous process and provide a set of axioms for its characterization. We establish both the uniqueness and existence of this process under our new formulation, with a key feature of these axioms being the matching of the first four moments. |
| title | Stochastic heat flow by moments |
| topic | Probability 82C27 (Primary) 60H17 (Secondary) |
| url | https://arxiv.org/abs/2410.14657 |