Before revision:  Results of numerical experiments then demonstrate that these asymptotic formulas agree qualitatively with Monte Carlo results for large finite networks, and quantitatively except when the  system is placed in an exceptional "knife-edge" configuration.
After revision:  Results of numerical experiments then demonstrate that these asymptotic formulas agree qualitatively with Monte Carlo results for large finite networks, and quantitatively except when the initial system is placed in an exceptional "knife-edge" configuration.