Arm Events in Two-Dimensional Invasion Percolation
Arm Events in Two-Dimensional Invasion Percolation
复制标题
二维入侵渗透中的手臂事件
DOI：
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发表时间：
2016
影响因子：
1.6
通讯作者：
Philippe Sosoe
中科院分区：
文献类型：
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作者：
M. Damron;Jack Hanson;Philippe Sosoe
我们比较了二维入侵渗流和临界渗流中“武器事件”的概率。臂事件由从原点到距离n的入侵和非入侵连接的规定“颜色序列”的存在来定义。我们发现，对于特定形式的序列，入侵渗透和临界渗透中的臂概率在n中是一致的，而它们在所有其他情况下相差n次幂。我们的结果的一个推论是，对于任何至少有两个开放（入侵）条目的颜色序列，在三角晶格上存在入侵渗透的臂指数。
We compare the probabilities of “arm events” in two-dimensional invasion percolation to those in critical percolation. Arm events are defined by the existence of a prescribed “color sequence” of invaded and non-invaded connections from the origin to distance n. We find that, for sequences of a particular form, arm probabilities in invasion percolation and critical percolation are comparable, uniformly in n, while they differ by a power of n for all others. A corollary of our results is the existence, on the triangular lattice, of arm exponents for invasion percolation, for any color sequence with at least two open (invaded) entries.