The trunks of CLE(4) explorations

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2023-10-01 DOI:10.1214/22-aap1895

Matthis Lehmkuehler

引用次数: 3

Abstract

The family of SLE4⟨μ⟩(−2) exploration processes with parameter μ∈R forms a natural class of conformally invariant ways for discovering the loops of a conformal loop ensemble CLE4. Such an exploration consists of one simple continuous path called the trunk of the exploration that discovers CLE4 loops along the way. The parameter μ appears in the Loewner chain description of the path that traces the trunk and all CLE4 loops encountered by the trunk in chronological order. These explorations can also be interpreted in terms of level lines of a Gaussian free field. It has been shown by Miller, Sheffield and Werner that the trunk of such an exploration is an SLE4(ρ,−2−ρ) process for some (unknown) value of ρ∈(−2,0). The main result of the present paper is to establish the relation between μ and ρ, more specifically to show that μ=−πcot(πρ/2).

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CLE(4)探索的主干

具有参数μ∈R的SLE4⟨μ⟩(−2)探索过程族形成了用于发现共形环系CLE4的环的共形不变方法的自然类别。这样的探索包括一条简单的连续路径，称为探索的主干，它在沿途发现CLE4环。参数μ出现在按照时间顺序跟踪干线和干线遇到的所有CLE4环路的路径的Loewner链描述中。这些探索也可以用高斯自由场的水平线来解释。Miller, Sheffield和Werner已经证明，对于ρ∈(- 2,0)的某个(未知)值，这种探索的主干是SLE4(ρ， - 2 - ρ)过程。本文的主要结果是建立了μ和ρ之间的关系，更具体地说，证明了μ=−πcot(πρ/2)。

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.