论文标题
$ \ mathbb {z}^2 $上的依赖性渗透
Dependent Percolation on $\mathbb{Z}^2$
论文作者
论文摘要
我们考虑了方形晶格$ \ mathbb {z}^2 $的依赖性渗透模型。依赖性范围是垂直和水平方向的无限范围。在这种情况下，我们证明了相变的存在。该证明利用了一个多尺度的重新归化参数，该参数被定义，一旦环境配置非常好，并且它与归纳步骤的主要估计一起来自Kesten，Sidoravicius和Vares（出现在{\ em Electonic of Proboreability of Probityability}中，（20222222222222年））。这项工作的灵感来自de Lima（博士学位，\ emph {infors deMatemática。Impa}，SérieC-26/2004），其中考虑了更简单的确定性环境情况。它具有各种应用程序，包括霍夫曼（{\ emComm。Math。phys。phys。} {\ bf 254}，1-22（2005））证明的二维随机拉伸晶格的相变的替代证明。
We consider a dependent percolation model on the square lattice $\mathbb{Z}^2$. The range of dependence is infinite in vertical and horizontal directions. In this context, we prove the existence of a phase transition. The proof exploits a multi-scale renormalization argument that is defined once the environment configuration is suitably good and, which, together with the main estimate for the induction step, comes from Kesten, Sidoravicius and Vares (To appear in {\em Electronic Journal of Probability}, (2022)). This work was inspired by de Lima (Ph.D.Thesis, \emph{Informes de Matemática. IMPA}, Série C-26/2004) where the simpler case of a deterministic environment was considered. It has various applications, including an alternative proof for the phase transition on the two dimensional random stretched lattice proved by Hoffman ({\em Comm. Math. Phys.} {\bf 254}, 1-22 (2005)).
