en
Scientific article
Open access
English

Sharp metastability threshold for an anisotropic bootstrap percolation model

Published inAnnals of probability, vol. 41, no. 3A, p. 1218-1242
Publication date2013
Abstract

Bootstrap percolation models have been extensively studied during the two past decades. In this article, we study the following "anisotropic" bootstrap percolation model: the neighborhood of a point (m,n) is the set [{(m+2,n),(m+1,n),(m,n+1),(m-1,n),(m-2,n),(m,n-1)}.] At time 0, sites are occupied with probability p. At each time step, sites that are occupied remain occupied, while sites that are not occupied become occupied if and only if three of more sites in their neighborhood are occupied. We prove that it exhibits a sharp metastability threshold. This is the first mathematical proof of a sharp threshold for an anisotropic bootstrap percolation model.

Classification
  • arxiv : math.PR
Citation (ISO format)
DUMINIL-COPIN, Hugo, VAN ENTER, A. C. D. Sharp metastability threshold for an anisotropic bootstrap percolation model. In: Annals of probability, 2013, vol. 41, n° 3A, p. 1218–1242. doi: 10.1214/11-AOP722
Main files (1)
Article (Accepted version)
accessLevelPublic
Identifiers
ISSN of the journal0091-1798
587views
204downloads

Technical informations

Creation10/20/2013 10:06:00 PM
First validation10/20/2013 10:06:00 PM
Update time03/14/2023 8:33:37 PM
Status update03/14/2023 8:33:37 PM
Last indexation01/16/2024 7:58:30 AM
All rights reserved by Archive ouverte UNIGE and the University of GenevaunigeBlack