论文标题
在非稳定环境中的连续渗透
Continuum Percolation in a Nonstabilizing Environment
论文作者
论文摘要
我们证明了基于COX点过程的布尔模型中连续渗透的相变，并具有非稳定导向度量。指导度量可以被视为经典泊松模型的固定随机环境，它是由平面矩形泊松线过程给出的。这种曼哈顿网格类型的结构具有在环境中的远程依赖性，导致相关的Cox-boolean模型没有尖锐的相变。相转换是在单独的以及共同变化的参数下建立的。我们的证据取决于离散的论点，以及与Hoffman 2005中建立的随机拉伸晶格的渗透的比较。
We prove phase transitions for continuum percolation in a Boolean model based on a Cox point process with nonstabilizing directing measure. The directing measure, which can be seen as a stationary random environment for the classical Poisson--Boolean model, is given by a planar rectangular Poisson line process. This Manhattan grid type construction features long-range dependencies in the environment, leading to absence of a sharp phase transition for the associated Cox--Boolean model. The phase transitions are established under individually as well as jointly varying parameters. Our proofs rest on discretization arguments and a comparison to percolation on randomly stretched lattices established in Hoffman 2005.
