Finite connections for supercritical Bernoulli bond percolation in 2D

2009/10/11 by Massimo Campanino, Campanino, Massimo, Dmitry Ioffe +3 · 1 citation
Mathematics · Physics and Astronomy · #FOS: Mathematics #FOS: Physical sciences #Markov Chains and Monte Carlo Methods #Mathematical Physics (math-ph) #Probability (math.PR) #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #math-ph #math.MP #math.PR

paper · pdf · doi:10.48550/arxiv.0910.1831

arxiv created 2009/10/11 · openalex publication_date 2009/10/11 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Two vertices are said to be finitely connected if they belong to the same cluster and this cluster is finite. We derive sharp asymptotics for finite connection probabilities for supercritical Bernoulli bond percolation on Z².

Citations

• Statistical mechanical methods in particle structure analysis of lattice field theories

Cited by

• Ornstein–Zernike behavior for Ising models with infinite-range interactions

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