平面GFF的厚点对于所有γ≠0都是完全不连通的

IF 1.3 3区数学 Q2 STATISTICS & PROBABILITY

Electronic Journal of Probability Pub Date : 2022-09-09 DOI:10.1214/23-ejp975

Juhan Aru, L'eonie Papon, E. Powell

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引用次数: 1

摘要

证明了具有Dirichlet边界条件的平面高斯自由场(GFF)的$\gamma$ -厚点集对于所有$\gamma \neq 0$都是完全不连通的。我们的证明依赖于GFF和嵌套CLE $_4$之间的耦合。特别是，我们证明了GFF的粗点与加权CLE $_4$嵌套域的粗点相同，并建立了嵌套CLE补的几乎肯定的完全不连通$_{\kappa}$, $\kappa \in (8/3,4]$。作为一个推论，我们看到超临界LQG指标的奇点集也是完全不连通的。

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Thick points of the planar GFF are totally disconnected for all γ≠0

We prove that the set of $\gamma$-thick points of a planar Gaussian free field (GFF) with Dirichlet boundary conditions is a.s. totally disconnected for all $\gamma \neq 0$. Our proof relies on the coupling between a GFF and the nested CLE$_4$. In particular, we show that the thick points of the GFF are the same as those of the weighted CLE$_4$ nesting field and establish the almost sure total disconnectedness of the complement of a nested CLE$_{\kappa}$, $\kappa \in (8/3,4]$. As a corollary we see that the set of singular points for supercritical LQG metrics is a.s. totally disconnected.

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来源期刊

Electronic Journal of Probability 数学-统计学与概率论

CiteScore

1.80

自引率

7.10%

发文量

119

审稿时长

4-8 weeks

期刊介绍： The Electronic Journal of Probability publishes full-size research articles in probability theory. The Electronic Communications in Probability (ECP), a sister journal of EJP, publishes short notes and research announcements in probability theory. Both ECP and EJP are official journals of the Institute of Mathematical Statistics and the Bernoulli society.