On critical phenomena in interacting growth systems. Part II: Bounded growth

This paper completes the classification of some infinite and finite growth systems which was started in Part I. Components whose states are integer numbers interact in a local deterministic way, in addition to which every component's state grows by a positive integerk with a probability ^k(1-) at every moment of the discrete time. Proposition 1 says that in the infinite system which starts from the state all zeros, percentages of elements whose states exceed a given valuek0 never exceed (C)^k, whereC=const. Proposition 2 refers to finite systems. It states that the same inequalities hold during a time which depends exponentially on the system size.