Erdos-Renyi random graphs + forest fires = self-organized criticality

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.

Version 3, dated 18 May 2009, final version, revised after referees' reports