Infinite Hierarchy of Exact Equations in the Bak-Sneppen Model
adap-org
2009-10-28 v1 Condensed Matter
Adaptation and Self-Organizing Systems
Exactly Solvable and Integrable Systems
solv-int
Abstract
We derive an infinite hierarchy of exact equations for the Bak-Sneppen model in arbitrary dimensions. These equations relate different moments of temporal duration and spatial size of avalanches. We prove that the exponents of the BS model are the same above and below the critical point and express the universal amplitude ratio of the avalanche spatial size in terms of the critical exponents. The equations uniquely determine the shape of the scaling function of the avalanche distribution. It is suggested that in the BS model there is only one independent critical exponent.
Cite
@article{arxiv.adap-org/9601003,
title = {Infinite Hierarchy of Exact Equations in the Bak-Sneppen Model},
author = {Sergei Maslov},
journal= {arXiv preprint arXiv:adap-org/9601003},
year = {2009}
}
Comments
Submitted to PRL, 4 two-column pages (revtex), 1 ps figure included with epsf, g-zipped, uuencoded