Stochastic heat flow by moments
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.
Cite
@article{arxiv.2410.14657,
title = {Stochastic heat flow by moments},
author = {Li-Cheng Tsai},
journal= {arXiv preprint arXiv:2410.14657},
year = {2026}
}
Comments
Definition 1.2(c) has been corrected. Accordingly, the assumptions of Theorem 1.9 and the 3rd and 4th lines of Section 4.2 have been slightly modified. The rest of the paper is unchanged. 29 pages, 3 figures