Critical length for semi-oriented bootstrap percolation
type: Item
instance of: scholarly article
title: Critical length for semi-oriented bootstrap percolation
zbMATH Open document ID: 0821.60092
DOI: 10.1016/0304-4149(94)00061-W
author: Thomas Mountford
published in: Stochastic Processes and their Applications
publication date: 1995-05-23T00:00:00Z
review text: The author studies two models of two-dimensional semi-oriented bootstrap percolation introduced by \textit{A. M. S. Duarte} [Physica A 157, 1075-1079 (1989)]. Let \(T_ N\) denote the set \([0,N]^ 2\) considered as a torus. Let \(p\) denote the probability of initial occupancy. Put \[ f(p) = \exp \bigl( (\log^ 2 p)/(1000p) \bigr),\;0 < p \leq 1, \quad \text{and} \quad g(p) = \exp \bigl( (1000 \log^ 2 p)/p \bigr),\;0 < p \leq 1. \] The main result of the present paper is the following: \[ \sup_{N \leq f(p)} P^ p (T_ N \text{ ``fills itself up'')} \to 0 \text{ as } p \to 0 \] and \[ \inf_{N \geq g(p)} P^ p(T_ N \text{ ``fills itself up'')} \to 1 \text{ as } p \to 0. \]
Mathematics Subject Classification ID: 60K35
zbMATH DE Number: 757527
zbMATH Keywords: critical lengths
zbMATH Keywords: exponential rates
zbMATH Keywords: bootstrap percolation
reviewed by: Klaus Schürger
MaRDI profile type: Publication
cites work: Metastability effects in bootstrap percolation
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cites work: Q5185817
cites work: Rates for the probability of large cubes being non-internally spanned in modified bootstrap percolation
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description: scientific article; zbMATH DE number 757527