On critical phenomena in interacting growth systems. Part II: Bounded growth
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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 ε k (1-ε) 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 valuek≥0 never exceed (Cε) 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.
Key WordsRandom process local interaction critical phenomena growth combinatorics contour method graph theory
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