当前位置: X-MOL 学术Indag. Math. › 论文详情
Our official English website, www.x-mol.net, welcomes your feedback! (Note: you will need to create a separate account there.)
Sharpness of the phase transition for the corrupted compass model on transitive graphs
Indagationes Mathematicae ( IF 0.6 ) Pub Date : 2021-04-01 , DOI: 10.1016/j.indag.2021.03.005
Thomas Beekenkamp

In the corrupted compass model on a vertex-transitive graph, a neighbouring edge of every vertex is chosen uniformly at random and opened. Additionally, with probability p, independently for every vertex, each of its neighbouring edges is opened. We study the size of open clusters in this model. Hirsch et al. (2018) have shown that for small p all open clusters are finite almost surely, while for large p, depending on the underlying graph, there exists an infinite open cluster almost surely. We show that the corresponding phase transition is sharp, i.e., in the subcritical regime, all open clusters are exponentially small. Furthermore we prove a mean-field lower bound in the supercritical regime. The proof uses the by now well established method based on the OSSS inequality. A second goal of this note is to showcase this method in an uncomplicated setting.



中文翻译:

传递图上损坏的罗盘模型的相变锐度

在顶点传递图上的损坏的罗盘模型中,每个顶点的相邻边随机地均匀选择并打开。另外,很有可能p,对于每个顶点,每个相邻的边都是独立打开的。我们在此模型中研究开放集群的大小。Hirsch等。(2018)已证明对于小p 几乎可以肯定,所有的开放星团都是有限的,而对于大型星团, p,取决于基础图,几乎可以肯定地存在一个无限的开放簇。我们表明,相应的相变是尖锐的,即在亚临界状态下,所有开放的团簇都呈指数减小。此外,我们证明了超临界状态下的平均场下界。该证明使用了目前基于OSSS不等式的成熟方法。本说明的第二个目标是在简单的环境中展示此方法。

更新日期:2021-04-20
down
wechat
bug