A random hierarchical lattice: The series-parallel graph and its properties

被引：19
|
作者：
Hambly, BM
Jordan, J
机构：
[1] Univ Oxford, Math Inst, Oxford OX2 3LB, England
[2] Univ Sheffield, Dept Probabil & Stat, Sheffield S3 7RH, S Yorkshire, England
来源：
ADVANCES IN APPLIED PROBABILITY | 2004年 / 36卷 / 03期
关键词：
hierarchical lattice; effective resistance; phase transition; first-passage percolation; Cheeger constants;
D O I：
10.1239/aap/1093962236
中图分类号：
O21 [概率论与数理统计]; C8 [统计学];
学科分类号：
020208 ; 070103 ; 0714 ;
摘要：
We consider a sequence of random graphs constructed by a hierarchical procedure. The construction replaces existing edges by pairs of edges in series or parallel with probability p. We investigate the effective resistance across the graphs, first-passage percolation on the graphs and the Cheeger constants of the graphs as the number of edges tends to infinity. In each case we find a phase transition at p = 1/2.
引用
收藏
页码：824 / 838
页数：15
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