The diameter of a long-range percolation cluster on generalized pre-Sierpinski carpet and regular tree
The diameter of a long-range percolation cluster on generalized pre-Sierpinski carpet and regular tree
复制标题
广义前谢尔宾斯基地毯和常规树上长程渗滤簇的直径
DOI：
10.1007/s10955-018-2181-z
复制
发表时间：
2019
影响因子：
1.6
通讯作者：
J. Misumi
中科院分区：
文献类型：
--
作者：
Nawata Norio;J. Misumi
我们考虑了几类由推广的pre-Sierpinski地毯，这是一个著名的分形格得到的图。在这里，我们不仅讨论了一些分形格，而且还讨论了许多不属于分形格的不规则图。在几个假设下，我们提出了估计的直径的长程渗流集群在这样的图。在Misumi（J Stat Phys 158：1083-1089，2015）中，对长程渗流簇的图直径的估计建立在另一种基本分形格的pre-Sierpinski gasket上，本文的结果是其在一定意义上的推广。我们还将讨论正则树上的长程渗流图的直径的行为，这似乎与广义pre-Sierpinski地毯上的结果有很大的不同。
We consider some kinds of graphs obtained by generalizing the pre-Sierpinski carpet, which is one of well known fractal lattices. Here, we deal with not only some fractal lattices, but also many irregular graphs which do not belong to fractal lattices. Under several assumptions, we present estimates on a diameter of the long-range percolation cluster on such graphs. In Misumi (J Stat Phys 158:1083–1089, 2015), estimates on the graph diameter of the long-range percolation cluster are established on the pre-Sierpinski gasket, which is another fundamental fractal lattice, and the result of this paper is its extension in a certain sense. We will also discuss the behavior of the diameter of the long-range percolation graph on a regular tree, which seems to be quite different from the result on the generalized pre-Sierpinski carpet.