Nearest-neighbor walks with low predictability profile and percolation in $2+\epsilon$ dimensions
Nearest-neighbor walks with low predictability profile and percolation in $2+\epsilon$ dimensions
复制标题
最近邻游走具有低可预测性和 $2 epsilon$ 维度的渗透
DOI：
10.1214/aop/1022855750
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发表时间：
1998
影响因子：
2.3
通讯作者：
Elchanan Mossel
中科院分区：
文献类型：
--
作者：
Olle Häggström;Elchanan Mossel
几年前，Grimmett，Kesten和Zhang证明了对于Z3上的超临界键渗流，无限团簇上的简单随机游动是a.s.短暂的我们将这一结果推广到Z3中的一类楔形，包括对任意e ∈（0，1），楔形W e = {（x，y，z）∈ Z3：x > 0，|z| < x e }，其可以被认为表示（2 + e）维晶格。我们的证明建立在Benjamini，Pemantle和Peres最近的工作，并涉及使用Z上的最近邻行走具有低可预测性的有限能量流的构建。沿着的方式，我们获得了一些新的结果，可预测性配置文件的最近邻行走的衰减率。
A few years ago, Grimmett, Kesten and Zhang proved that for supercritical bond percolation on Z 3 , simple random walk on the infinite cluster is a.s. transient. We generalize this result to a class of wedges in Z 3 including, for any e ∈ (0,1), the wedge W e = {(x, y, z) ∈ Z 3 : x > 0, |z| < x e } which can be thought of as representing a (2 + e)-dimensional lattice. Our proof builds on recent work of Benjamini, Pemantle and Peres, and involves the construction of finite-energy flows using nearest-neighbor walks on Z with low predictability profile. Along the way, we obtain some new results on attainable decay rates for predictability profiles of nearest-neighbor walks.