Absence of Infinite Cluster for Critical Bernoulli Percolation on Slabs

被引：14

作者：

Duminil-Copin, Hugo ^{[1
]}

Sidoravicius, Vladas ^{[2
,3
,4
]}

Tassion, Vincent ^{[1
,5
]}

机构：

[1] Univ Geneva, Dept Math, 2-4 Rue Lievre,Case Postale 64, CH-1211 Geneva 4, Switzerland

[2] IMPA, Estr Dona Castorina 110, BR-22460320 Rio De Janeiro, RJ, Brazil

[3] Courant Inst, 251 Mercer St, New York, NY 10012 USA

[4] NYU Shanghai, Math Res Inst, NYU ECNU, Shanghai, Peoples R China

[5] Ecole Normale Super Lyon, Lyon, France

来源：

COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS | 2016年 / 69卷 / 07期

基金：

瑞士国家科学基金会;

关键词：

UNIQUENESS; CONTINUITY; DENSITY; SQUARE; PHASE; MODEL;

D O I：

10.1002/cpa.21641

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We prove that for Bernoulli percolation on a graph Z(2) x {0, ... , k} (k >= 0), there is no infinite cluster at criticality, almost surely. The proof extends to finite-range Bernoulli percolation models on Z(2) that are invariant under pi/2-rotation and reflection. (C) 2016 Wiley Periodicals, Inc.

引用

页码：1397 / 1411

页数：15

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