Triangle condition for oriented percolation in high dimensions
type: Item
instance of: scholarly article
title: Triangle condition for oriented percolation in high dimensions
zbMATH Open document ID: 0806.60097
author: Bao Gia Nguyen
author: Wei-Shih Yang
published in: The Annals of Probability
publication date: 1995-02-12T00:00:00Z
review text: By verifying the triangle condition, \textit{T. Hara} and \textit{G. Slade} [Commun. Math. Phys. 128, No. 2, 333-391 (1990; Zbl 0698.60100)] proved mean-field behaviour of the percolation model both for the spread-out model in seven or more dimensions, and for the usual nearest-neighbour model in sufficiently many dimensions. The corresponding program is reported in the current paper, in the case of oriented percolation. This is achieved by a modification of the arguments of Hara and Slade. In the case of oriented percolation, the upper critical dimension is thought to be \(4 + 1\), and this is supported by the proof of mean-field behaviour for the spread-out model on \(\mathbb{Z}^ 5 \times \mathbb{Z}\).
reviewed by: G. R. Grimmett
Mathematics Subject Classification ID: 60K35
Mathematics Subject Classification ID: 82B43
zbMATH DE Number: 528622
zbMATH Keywords: triangle condition
zbMATH Keywords: mean-field behaviour
zbMATH Keywords: percolation model
zbMATH Keywords: nearest- neighbour model
zbMATH Keywords: oriented percolation
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1214/aop/1176989001
OpenAlex ID: W2049651736
DOI: 10.1214/AOP/1176989001
description: scientific article; zbMATH DE number 528622