Approximate zero-one laws and sharpness of the percolation transition in a class of models including two-dimensional Ising percolation
type: Item
instance of: scholarly article
title: Approximate zero-one laws and sharpness of the percolation transition in a class of models including two-dimensional Ising percolation
zbMATH Open document ID: 1155.60044
DOI: 10.1214/07-AOP380
published in: The Annals of Probability
publication date: 2008-10-20T00:00:00Z
full work available at URL: https://arxiv.org/abs/0809.4184
review text: If \(p\) denotes the critical probability for bond percolation, and \(q\) is the critical probability for the matching lattice of the square lattice, then one has the equality \(p+q=1\). The present paper shows that this relation \(p+q=1\) holds for a large class of weakly dependent two-dimension percolation models, which are endowed with representation in terms of i.i.d. random variables. The key in the proof of this result is a new approximate zero-one law.
Mathematics Subject Classification ID: 60K35
Mathematics Subject Classification ID: 82B43
zbMATH DE Number: 5353659
zbMATH Keywords: percolation
zbMATH Keywords: RSW
zbMATH Keywords: sharp transition
zbMATH Keywords: approximate zero-one
zbMATH Keywords: sharp thresholds
author: Jacob van den Berg
reviewed by: Guy Jumarie
MaRDI profile type: Publication
arXiv ID: 0809.4184
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OpenAlex ID: W3102461391
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