Loop-erased random walk branch of uniform spanning tree in topological polygons

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2021-08-24 DOI:10.3150/22-bej1510

Mingchang Liu, Hao Wu

引用次数: 1

Abstract

We consider uniform spanning tree (UST) in topological polygons with $2N$ marked points on the boundary with alternating boundary conditions. In [LPW21], the authors derive the scaling limit of the Peano curve in the UST. They are variants of SLE$_8$. In this article, we derive the scaling limit of the loop-erased random walk branch (LERW) in the UST. They are variants of SLE$_2$. The conclusion is a generalization of [HLW20,Theorem 1.6] where the authors derive the scaling limit of the LERW branch of UST when $N=2$. When $N=2$, the limiting law is SLE$_2(-1,-1; -1, -1)$. However, the limiting law is nolonger in the family of SLE$_2(\rho)$ process as long as $N\ge 3$.

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拓扑多边形一致生成树的环擦除随机行走分支

在交替边界条件下，我们考虑边界上有$2N$个标记点的拓扑多边形中的一致生成树（UST）。在[LPW21]中，作者推导了UST中Peano曲线的比例极限。它们是SLE$_8$的变体。在本文中，我们推导了UST中循环擦除随机游动分支（LERW）的缩放极限。它们是SLE$_2$的变体。该结论是[HLW20，定理1.6]的推广，其中作者推导了当$N=2$时UST的LERW分支的标度极限。当$N=2$时，极限律为SLE$_2（-1，-1；-1，-1）$。然而，在SLE$_2（\rho）$过程的族中，只要$N\ge3$，限制律就不存在。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.