论文标题
有优先方向的角渗透
Corner percolation with preferential directions
论文作者
论文摘要
Corner Percolation是BálintTóth引入的Z^2上的依赖键渗透模型，其中每个顶点恰好具有两个垂直于彼此的入射边缘。加伯·皮特（GáborPete）在2008年已证明，在最大熵概率措施下，所有连接的组件几乎都是有限的循环。我们在这里考虑一个概率P和Q的首选西方和北方方向的制度，（p，q）与（1/2,1/2）不同。我们证明，几乎肯定存在无限数量的无限连接组件，实际上是无限的路径。此外，它们都具有相同的渐近斜率（2Q-1）/（1-2p）。
Corner percolation is a dependent bond percolation model on Z^2 introduced by Bálint Tóth, in which each vertex has exactly two incident edges, perpendicular to each other. Gábor Pete has proven in 2008 that under the maximal entropy probability measure, all connected components are finite cycles almost surely. We consider here a regime where West and North directions are preferred with probability p and q respectively, with (p,q) different from (1/2,1/2). We prove that there exists almost surely an infinite number of infinite connected components, which are in fact infinite paths. Furthermore, they all have the same asymptotic slope (2q-1)/(1-2p).
