Bounds for avalanche critical values of the Bak-Sneppen model
| dc.creator | Gillett, Alexis | |
| dc.creator | Meester, Ronald | |
| dc.creator | Nuyens, Misja | |
| dc.date | 2005-08-09 | |
| dc.date | 2006-03-30 | |
| dc.date.accessioned | 2026-07-07T06:42:46Z | |
| dc.date.available | 2026-07-07T06:42:46Z | |
| dc.description | We study the Bak-Sneppen model on locally finite transitive graphs $G$, in particular on Z^d and on T_Delta, the regular tree with common degree Delta. We show that the avalanches of the Bak-Sneppen model dominate independent site percolation, in a sense to be made precise. Since avalanches of the Bak-Sneppen model are dominated by a simple branching process, this yields upper and lower bounds for the so-called avalanche critical value $p_c^{BS}(G)$. Our main results imply that 1/(Delta+1) <= \leq p_c^{BS}(T_Delta) \leq 1/(Delta -1)$, and that $1/(2d+1)\leq p_c^{BS}(Z^d)\leq 1/(2d)+ 1/(2d)^2+O(d^{-3}), as d\to\infty. | |
| dc.description | 19 pages | |
| dc.identifier | https://arxiv.org/abs/math/0508167 | |
| dc.identifier | http://arxiv.org/abs/math/0508167 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/102162 | |
| dc.subject | Probability | |
| dc.subject | Mathematical Physics | |
| dc.subject | 60K35, 82B43 (primary); 60J80, 82C22 (secondary) | |
| dc.title | Bounds for avalanche critical values of the Bak-Sneppen model | |
| dc.type | text |