Article (320 Kb) - 
Free access
Highlights
More informations
Scientific Article
unige:30542 
 |
Sharp metastability threshold for an anisotropic bootstrap percolation model |
|
| Authors | ||
| 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 | DOI: 10.1214/11-AOP722 arXiv: 1010.4691 | |
| Full text | ||
| 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 |
282 hits 
83 downloads 
Contact an author
Update