论文标题
露台的渗透和矫正模型的增强
Percolation of terraces, and enhancements for the orthant model
论文作者
论文摘要
我们研究了I.I.D.的模型〜一般维度的随机环境$ d \ ge 2 $，每个站点都配备了两个环境之一。该模型带有一个参数$ p $，该参数控制了第一个环境的频率，对于每个维度$ d $，都有一个关键参数$ p_c（d）$，在该参数中有一个特定连接群集的几何形状的相变（群集是无限的$ p $）。我们在这种小说环境中使用了著名的增强方法，以证明$ p_c（d）$在$ d $中严格单调。为此，我们研究了称为梯田的高维结构的离散几何形状和渗透理论。
We study a model of an i.i.d.~random environment in general dimensions $d\ge 2$, where each site is equipped with one of two environments. The model comes with a parameter $p$ which governs the frequency of the first environment, and for each dimension $d$ there is a critical parameter $p_c(d)$ at which there is a phase transition for the geometry of a particular connected cluster (the cluster is infinite for all $p$). We use the celebrated methodology of enhancements in this novel setting to prove that $p_c(d)$ is strictly monotone in $d$ for this model. To do so we study the discrete geometry and percolation theory of higher-dimensional structures called terraces.
