Exact results for one dimensional stochastic cellular automata for different types of updates

Details Exact results for one dimensional stochastic cellular automata for different types of updates Exact results for one dimensional stochastic cellular automata for different types of updates

1996-11-20

arxiv.org/abs/cond-mat/9611154v1

Physics

Condensed Matter

Statistical Mechanics

7 pages, Latex

Scientific paper

We study two common types of time-noncontinuous updates for one dimensional stochastic cellular automata with arbitrary nearest neighbor interactions and arbitrary open boundary conditions. We first construct the stationary states using the matrix product formalism. This construction then allows to prove a general connection between the stationary states which are produced by the two different types of updates. Using this connection, we derive explicit relations between the densities and correlation functions for these different stationary states.

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