The Metastability Threshold for Modified Bootstrap Percolation in d Dimensions
| dc.creator | Holroyd, Alexander E. | |
| dc.date | 2006-03-28 | |
| dc.date | 2006-04-03 | |
| dc.date.accessioned | 2026-07-07T07:07:16Z | |
| dc.date.available | 2026-07-07T07:07:16Z | |
| dc.description | In the modified bootstrap percolation model, sites in the cube {1,...,L}^d are initially declared active independently with probability p. At subsequent steps, an inactive site becomes active if it has at least one active nearest neighbour in each of the d dimensions, while an active site remains active forever. We study the probability that the entire cube is eventually active. For all d>=2 we prove that as L\to\infty and p\to 0 simultaneously, this probability converges to 1 if L=exp^{d-1} (lambda+epsilon)/p, and converges to 0 if L=exp^{d-1} (lambda-epsilon)/p, for any epsilon>0. Here exp^n denotes the n-th iterate of the exponential function, and the threshold lambda equals pi^2/6 for all d. | |
| dc.description | 20 pages, 3 figures (added discussion, corrected typo in (24)) | |
| dc.identifier | https://arxiv.org/abs/math/0603645 | |
| dc.identifier | http://arxiv.org/abs/math/0603645 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/110331 | |
| dc.subject | Probability | |
| dc.subject | Mathematical Physics | |
| dc.subject | 60K35; 82B43 | |
| dc.title | The Metastability Threshold for Modified Bootstrap Percolation in d Dimensions | |
| dc.type | text |