Long-range percolation on the hierarchical lattice

被引：6

作者：

Koval, Vyacheslav ^{[1
]}

Meester, Ronald ^{[2
]}

Trapman, Pieter ^{[3
]}

机构：

[1] Univ Utrecht, NL-3508 TC Utrecht, Netherlands

[2] Vrije Univ Amsterdam, Amsterdam, Netherlands

[3] Stockholm Univ, Stockholm, Sweden

来源：

ELECTRONIC JOURNAL OF PROBABILITY | 2012年 / 17卷

关键词：

long-range percolation; renormalisation; ergodicity; PHASE-TRANSITION; MODELS; EPIDEMICS; GRAPH;

D O I：

10.1214/EJP.v17-1977

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 study long-range percolation on the hierarchical lattice of order N, where any edge of length k is present with probability p(k) = 1 - exp (-beta(-k)alpha), independently of all other edges. For fixed beta, we show that alpha(c)(beta) ( the infimum of those alpha for which an infinite cluster exists a.s.) is non-trivial if and only if N < beta < N-2. Furthermore, we show uniqueness of the infinite component and continuity of the percolation probability and of alpha(c)(beta) as a function of beta. This means that the phase diagram of this model is well understood

引用

页码：1 / 21

页数：21

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