TY - GEN
A1 - Louis, Pierre-Yves
T1 - Ergodicity of PCA
BT - equivalence between spatial and temporal mixing conditions
N2 - For a general attractive Probabilistic Cellular Automata on S-Zd, 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), wit a naturally associated Gibbsian potential rho, we prove that a (spatial-) weak mixing condition (WM) for rho implies the validity of the assumption (A); thus exponential (time-) ergodicity of these dynamics towards the unique Gibbs measure associated to rho hods. On some particular examples we state that exponential ergodicity holds as soon as there is no phase transition.
KW - Wahrscheinlichkeitstheorie
KW - Wechselwirkende Teilchensysteme
KW - Stochastische Zellulare Automaten
KW - Interacting particle systems
KW - Probabilistic Cellular Automata
KW - ERgodicity of Markov Chains
KW - Gibbs measures
Y1 - 2004
U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-6589
ER -
TY - GEN
A1 - Louis, Pierre-Yves
T1 - Increasing coupling for probabilistic cellular automata
N2 - We give a necessary and sufficient condition for the existence of an increasing coupling of N (N >= 2) synchronous dynamics on S-Zd (PCA). Increasing means the coupling preserves stochastic ordering. We first present our main construction theorem in the case where S is totally ordered; applications to attractive PCAs are given. When S is only partially ordered, we show on two examples that a coupling of more than two synchronous dynamics may not exist. We also prove an extension of our main result for a particular class of partially ordered spaces.
KW - Wahrscheinlichkeitstheorie
KW - stochastische Anordnung
KW - stochastische Zellulare Automaten
KW - Kopplung
KW - stochastic ordering
KW - Probabilistic Cellular Automata
KW - monotone coupling
Y1 - 2005
U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-6593
ER -