Bounds for avalanche critical values of the Bak-Sneppen model
Gillett, Alexis ; Meester, Ronald ; Nuyens, Misja
arXiv, 0508167 / Harvested from arXiv
Text on arXiv
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.
Publié le : 2005-08-09
Classification:  Mathematics - Probability,  Mathematical Physics,  60K35, 82B43 (primary),  60J80, 82C22 (secondary) 
@article{0508167,
     author = {Gillett, Alexis and Meester, Ronald and Nuyens, Misja},
     title = {Bounds for avalanche critical values of the Bak-Sneppen model},
     journal = {arXiv},
     volume = {2005},
     number = {0},
     year = {2005},
     language = {en},
     url = {http://dml.mathdoc.fr/item/0508167}
}

Gillett, Alexis; Meester, Ronald; Nuyens, Misja. Bounds for avalanche critical values of the Bak-Sneppen model. arXiv, Tome 2005 (2005) no. 0, . http://gdmltest.u-ga.fr/item/0508167/