Dependent percolation on Z2

被引：2

作者：

de Lima, Bernardo N. B. ^{[1
]}

Sidoravicius, Vladas ^{[2
]}

Vares, Maria Eulalia ^{[3
]}

机构：

[1] Univ Fed Minas Gerais, Dept Matemat, Av Antonio Carlos 6627, BR-30123970 Belo Horizonte, MG, Brazil

[2] Shanghai New York Univ, Shanghai, Peoples R China

[3] Univ Fed Rio De Janeiro, Inst Matemat, Av Athos da Silveira Ramos 149, BR-21941909 Rio De Janeiro, RJ, Brazil

来源：

BRAZILIAN JOURNAL OF PROBABILITY AND STATISTICS | 2023年 / 37卷 / 02期

关键词：

Dependent percolation; multiscale renormalization; random environment; 2-DIMENSIONAL ISING-MODEL; RANDOM IMPURITIES;

D O I：

10.1214/23-BJPS575

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 dependent percolation model on the square lattice Z2. The range of dependence is infinite in vertical and horizontal directions. In this context, we prove the existence of a phase transition. The proof exploits a multi-scale renormalization argument that is defined once the environment configuration is suitably good and, which, together with the main estimate for the induction step, comes from Kesten, Sidoravicius and Vares (Electronic Journal of Probability 27 (2022) 1-49). This paper is inspired where the simpler case of a deterministic environment was considered. It has various applications, including an alternative proof for the phase transition on the two dimensional random stretched lattice proved by Hoffman (Comm. Math. Phys. 254 (2005) 1-22).

引用

页码：431 / 454

页数：24

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