Absence of Site Percolation at Criticality in Z2 x {0,1}

被引：1

作者：

Damron, Michael ^{[1
]}

Newman, Charles M. ^{[2
,3
]}

Sidoravicius, Vladas ^{[4
]}

机构：

[1] Princeton Univ, Dept Math, Princeton, NJ 08544 USA

[2] NYU, Courant Inst, New York, NY USA

[3] Univ Calif Irvine, Irvine, CA 92717 USA

[4] IMPA, BR-22460320 Rio De Janeiro, Brazil

来源：

RANDOM STRUCTURES & ALGORITHMS | 2015年 / 47卷 / 02期

基金：

美国国家科学基金会;

关键词：

critical percolation; slab percolation; sandwich percolation; two dimensions;

D O I：

10.1002/rsa.20544

中图分类号：

TP31 [计算机软件];

学科分类号：

081202 ; 0835 ;

摘要：

In this note we consider site percolation on a two dimensional sandwich of thickness two, the graph Z2x{0,1}. We prove that there is no percolation at the critical point. The same arguments are valid for a sandwich of thickness three with periodic boundary conditions. It remains an open problem to extend this result to other sandwiches. Note added in proof: This extension has recently been accomplished in arXiv 1401.7130. (c) 2014 Wiley Periodicals, Inc. Random Struct. Alg., 47, 328-340, 2015

引用

页码：328 / 340

页数：13

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