发表机构
University of Utah; North Carolina State University; Boston University（犹他大学; 北卡罗来纳州立大学; 波士顿大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究建立了关联两点自由能相关空间导数与聚合物几何量的恒等式，利用对称性和无记忆性推导，应用于恢复伯克性质及得到布朗最后通行渗流的对应恒等式。
AI 中文摘要
我们建立了一个恒等式，将两点自由能相关的空间导数与两个基本几何量关联起来：一是在同一环境中独立采样的两条聚合物在到达规定终端水平前相遇的退火概率，二是单条聚合物的出口点位置。该结果部分受Gu和Quastel近期针对KPZ方程的分部积分工作启发，他们连续情形下的关键步骤依赖于Itô公式的巧妙应用，而这在我们的半离散情形中无直接对应，因此我们利用聚合物模型的内在对称性与无记忆性进行推导。我们还给出两个应用：(i)通过证明锚定的平稳水平自由能轮廓是双侧布朗运动，恢复了水平伯克性质；(ii)在零温度极限下，得到了布朗最后通行渗流的对应恒等式。
英文摘要
We establish an identity relating the spatial derivative of a two-point free-energy correlation to two fundamental geometric quantities: the annealed probability that two independently sampled polymers, in the same environment, meet before reaching the prescribed terminal level, and the exit-point location of a single polymer. Our result is inspired in part by recent integration-by-parts work of Gu and Quastel for the KPZ equation. A crucial step in their continuous setting relies on an ingenious application of Itô's formula, which has no direct analogue in our semi-discrete setting. Instead, we exploit intrinsic symmetries of the polymer model together with the memoryless property. We also provide two applications: (i) we recover the horizontal Burke property by proving that the anchored stationary horizontal free-energy profile is a two-sided Brownian motion; (ii) in the zero-temperature limit, we obtain the corresponding identity for Brownian last-passage percolation.
Comments43 pages, 5 figures
