Distribution of local magnetisations in random networks of automata

The authors derive an integral equation which gives the distribution P(m) of local magnetisations for a random network of automata (Kauffman model). They show how from this distribution one can recover the distances between configurations and the fraction of spins in the stable core (i.e. the spins which do not depend on the initial conditions). A numerical solution of the integral equation shows that P(m) has singularities at m=0, +or-1/2 and +or-1.