Journal of Statistical Physics

, Volume 74, Issue 1–2, pp 111–130 | Cite as

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

  • Andrei Toom


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 Words

Random process local interaction critical phenomena growth combinatorics contour method graph theory 


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  1. 1.
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    Andrei Toom, On critical phenomena in interacting growth systems. Part I: General,J. Stat. Phys., this issue.Google Scholar

Copyright information

© Plenum Publishing Corporation 1994

Authors and Affiliations

  • Andrei Toom
    • 1
  1. 1.Incarnate Word CollegeSan Antonio

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