Erin Russell

Playing with Fire: The Necessary Evil of Self-organised Criticality

Consider a mean field Erdős-Rényi random digraph process on n vertices. Let each possible directed edge arrive with rate 1/n. Without opposition, this process is guaranteed to result in the n-complete graph. Hence, we introduce a Poisson rain of “lightning strikes” to each vertex with rate λ(n) which propagates across its out-graph, burning all edges of an affected vertex. Subsequently, the system continues to fluctuate to no end in a battle between creation and destruction.