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arXiv · 2410.14657

Stochastic heat flow by moments

Li-Cheng Tsai
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Abstract

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.

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Li-Cheng Tsai. 2024-10-18. Stochastic heat flow by moments. https://arxiv.org/abs/2410.14657

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