Stavskaya's Measure Is Weakly Gibbsian
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