On critical phenomena in interacting growth systems. Part II: Bounded growth |
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Authors: | Andrei Toom |
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Institution: | (1) Incarnate Word College, 78209 San Antonio, Texas |
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Abstract: | 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 valuek 0 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. |
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Keywords: | Random process local interaction critical phenomena growth combinatorics contour method graph theory |
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