The scaling limits of near-critical and dynamical percolation
The scaling limits of near-critical and dynamical percolation
复制标题
近临界和动态渗透的缩放极限
DOI：
10.4171/jems/786
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发表时间：
2013
期刊：
影响因子：
--
通讯作者：
O. Schramm
中科院分区：
文献类型：
--
作者：
C. Garban;G. Pete;O. Schramm
我们证明了在Schramm和Smirnov引入的渗流构型的“四交叉”空间$\mathcal{H}$中，三角晶格$\eta \mathbb{T}$上的近临界渗流和动态渗流具有一个尺度极限，即网格$\eta \到0$。证明基本上是通过“扰动”临界模型的缩放极限来进行的，使用了我们之前论文中研究的关键度量。并建立了这些新的极限对象的马尔可夫性和保形协方差。
We prove that near-critical percolation and dynamical percolation on the triangular lattice $\eta \mathbb{T}$ have a scaling limit as the mesh $\eta \to 0$, in the "quad-crossing" space $\mathcal{H}$ of percolation configurations introduced by Schramm and Smirnov. The proof essentially proceeds by "perturbing" the scaling limit of the critical model, using the pivotal measures studied in our earlier paper. Markovianity and conformal covariance of these new limiting objects are also established.