CLE(4)探索的主干

IF 1.4 2区数学 Q2 STATISTICS & PROBABILITY

Annals of Applied Probability Pub Date : 2023-10-01 DOI:10.1214/22-aap1895

Matthis Lehmkuehler

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引用次数: 3

摘要

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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The trunks of CLE(4) explorations

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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来源期刊

Annals of Applied Probability 数学-统计学与概率论

CiteScore

2.70

自引率

5.60%

发文量

108

审稿时长

6-12 weeks

期刊介绍： The Annals of Applied Probability aims to publish research of the highest quality reflecting the varied facets of contemporary Applied Probability. Primary emphasis is placed on importance and originality.