论文标题
基于循环的随机步行作为可观察的自旋系统
Loop-erased random walk as a spin system observable
论文作者
论文摘要
基于环的随机步行的缩放限制的Hausdorff尺寸的确定与研究基于环的随机行走的单点函数的研究密切相关，即，基于环的随机步行通过给定的顶点概率。理论物理学文献中的最新工作通过将田间理论技术应用于研究旋转系统的启发式编码基于环的随机步行的单点函数的旋转系统，研究了基于环的随机步行的Hausdorff维度。受此启发的启发，我们引入了两个不同的自旋系统，它们的相关函数可以严格证明，以编码基于环的随机步行的单点函数。
The determination of the Hausdorff dimension of the scaling limit of loop-erased random walk is closely related to the study of the one-point function of loop-erased random walk, i.e., the probability a loop-erased random walk passes through a given vertex. Recent work in the theoretical physics literature has investigated the Hausdorff dimension of loop-erased random walk in three dimensions by applying field theory techniques to study spin systems that heuristically encode the one-point function of loop-erased random walk. Inspired by this, we introduce two different spin systems whose correlation functions can be rigorously shown to encode the one-point function of loop-erased random walk.
