Erdos-Renyi random graphs + forest fires = self-organized criticality
Probability
2009-08-26 v3 Mathematical Physics
math.MP
Abstract
We modify the usual Erdos-Renyi random graph evolution by letting connected clusters 'burn down' (i.e. fall apart to disconnected single sites) due to a Poisson flow of lightnings. In a range of the intensity of rate of lightnings the system sticks to a permanent critical state.
Cite
@article{arxiv.0808.2116,
title = {Erdos-Renyi random graphs + forest fires = self-organized criticality},
author = {Balazs Rath and Balint Toth},
journal= {arXiv preprint arXiv:0808.2116},
year = {2009}
}
Comments
Version 3, dated 18 May 2009, final version, revised after referees' reports