Erdös-Rényi random graphs + forest fires = self-organized criticality

Abstract

We modify the usual Erdös-Rényi 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. © 2009 Applied Probability Trust.