Parabolic Harnack Inequality and Local Limit Theorem for Percolation Clusters
Parabolic Harnack Inequality and Local Limit Theorem for Percolation Clusters
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DOI：
10.1214/ejp.v14-587
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发表时间：
2008-10
影响因子：
1.4
通讯作者：
M. Barlow;B. Hambly
中科院分区：
文献类型：
--
作者：
M. Barlow;B. Hambly
我们考虑 $\mathbb{Z}^d$ 中超临界渗流簇的随机游走。之前的论文已经获得了高斯热核边界，以及 a.s.这个过程的不变性原则。我们展示了这些信息如何导致抛物线哈纳克不等式、局部极限定理和格林函数的估计。
We consider the random walk on supercritical percolation clusters in $\mathbb{Z}^d$. Previous papers have obtained Gaussian heat kernel bounds, and a.s. invariance principles for this process. We show how this information leads to a parabolic Harnack inequality, a local limit theorem and estimates on the Green's function.