通过矩方法研究临界随机热流（SHF）的连续时间定向聚合物
Continuous-time directed polymers to the Critical SHF via moments
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中文总结 AI 辅助
本文针对关联布朗环境中的二维连续时间定向随机聚合物，利用矩方法证明其配分函数收敛到临界随机热流（SHF），为临界SHF的离散近似提供了收敛性理论支撑。
中文摘要 AI 辅助
我们研究关联布朗环境中一类二维连续时间定向随机聚合物，这类聚合物的配分函数构成了Caravenna、Sun和Zygouras（2023）构造的临界随机热流（Critical Stochastic Heat Flow, SHF）的离散近似。利用Tsai（2024）近期提出的基于矩的SHF公理化刻画，我们证明了作为随机测度的点对点配分函数收敛到临界SHF。证明过程分为两步：首先通过Gu、Quastel和Tsai（2021）引入的、基于Rajeev（1999）及Dimock和Rajeev（2004）的预解式方法，建立所有矩的收敛性；随后建立紧性并验证刻画中的剩余公理。
英文摘要
We consider a class of two-dimensional continuous-time directed random polymers in a correlated Brownian environment. The partition functions of these polymers form a discrete approximation of the Critical Stochastic Heat Flow (SHF), constructed by Caravenna, Sun and Zygouras (2023). Using a recent moment based axiomatic characterization of the SHF by Tsai (2024), we prove that the point-to-point partition functions, viewed as random measures, converge to the critical SHF. The proof proceeds by first establishing convergence of all moments through the resolvent method introduced by Gu, Quastel and Tsai (2021) and based on Rajeev (1999) and Dimock and Rajeev (2004). This is followed by establishing tightness and verifying the remaining axioms in the characterization.
