Bounds for avalanche critical values of the Bak-Sneppen model

dc.creatorGillett, Alexis
dc.creatorMeester, Ronald
dc.creatorNuyens, Misja
dc.date2005-08-09
dc.date2006-03-30
dc.date.accessioned2026-07-07T06:42:46Z
dc.date.available2026-07-07T06:42:46Z
dc.descriptionWe 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.description19 pages
dc.identifierhttps://arxiv.org/abs/math/0508167
dc.identifierhttp://arxiv.org/abs/math/0508167
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/102162
dc.subjectProbability
dc.subjectMathematical Physics
dc.subject60K35, 82B43 (primary); 60J80, 82C22 (secondary)
dc.titleBounds for avalanche critical values of the Bak-Sneppen model
dc.typetext

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