Stavskaya's Measure Is Weakly Gibbsian

J. Depoorter, C. Maes

2006, v.12, Issue 4, 791-804


Stavskaya's model is a one-dimensional Boolean probabilistic cellular automaton very similar to the contact and directed percolation processes. There is always an absorbing measure but close to the deterministic limit the model also shows a non-trivial invariant measure. We show that the latter "Stavskaya's" measure is weakly Gibbsian with an exponentially decaying interaction potential.

Keywords: probabilistic cellular automata,Gibbs measure


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