TY  - JOUR
A1  - Louis, Pierre-Yves
T1  - Ergodicity of PCA: equivalence between spatial and temporal mixing conditions
N2  - For a general attractive Probabilistic Cellular Automata on SZd, we prove that the (time-) convergence towards equilibrium of this Markovian parallel dynamics exponentially fast in the uniform norm is equivalent to a condition (A). This condition means the exponential decay of the influence from the boundary for the invariant measures of the system restricted to finite boxes. For a class of reversible PCA dynamics on {;1, +1}Zd, with a naturally associated Gibbsian potential ;, we prove that a (spatial-) weak mixing condition (WM) for ; implies the validity of the assumption (A); thus exponential (time-) ergodicity of these dynamics towards the unique Gibbs measure associated to ; holds. On some particular examples we state that exponential ergodicity holds as soon as there is no phase transition.
Y1  - 2004
UR  - http://www.math.washington.edu/%7Eejpecp/ECP/viewarticle.php?id=1704&layout=abstract
ER  -