亚临界长程随机聚类和波茨模型中相关函数的尖锐渐近性

arXiv: Probability Pub Date : 2020-06-30 DOI:10.1214/21-ECP390

Y. Aoun

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引用次数: 5

摘要

对于一类簇权为$q\geq 1$的随机聚类模型，我们证明了$0$与$x$相连接的概率渐近等于$\tfrac{1}{q}\chi(\beta)^{2}\beta J_{0,x}$。本文提出的方法可以应用于任何存在单单调随机簇表示的自旋模型。

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Sharp asymptotics of correlation functions in the subcritical long-range random-cluster and Potts models

For a family of random-cluster models with cluster weights $q\geq 1$, we prove that the probability that $0$ is connected to $x$ is asymptotically equal to $\tfrac{1}{q}\chi(\beta)^{2}\beta J_{0,x}$. The method developed in this article can be applied to any spin model for which there exists a random-cluster representation which is one-monotonic.

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来源期刊

arXiv: Probability

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