UNIGE document Scientific Article
previous document  unige:30542  next document
add to browser collection
Title

Sharp metastability threshold for an anisotropic bootstrap percolation model

Authors
Van Enter, A. C. D.
Published in Annals of Probability. 2013, vol. 41, no. 3A, p. 1218-1242
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.
Identifiers
arXiv: 1010.4691
Full text
Article (320 Kb) - public document Free access
Structures
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. https://archive-ouverte.unige.ch/unige:30542

205 hits

59 downloads

Update

Deposited on : 2013-10-21

Export document
Format :
Citation style :