Pierre-Yves Louis

STATIONARY MEASURES AND PHASE TRANSITION FOR A CLASS OF PROBABILISTIC CELLULAR AUTOMATA

We discuss various properties of Probabilistic Cellular Automata, such as the structure of the set of stationary measures and multiplicity of stationary measures (or phase transition) for reversible models.

Ergodicity of PCA: Equivalence between Spatial and Temporal Mixing Conditions

For a general attractive Probabilistic Cellular Automata on

Synchronization via Interacting Reinforcement

S^{\mathbb{Z}^d}

Effect of self-interaction on the phase diagram of a Gibbs-like measure derived by a reversible Probabilistic Cellular Automata

, we prove that the (time-) convergence towards equilibrium of this Markovian parallel dynamics, exponentially fast in the uniform norm, is equivalent to a condition (

Realizable monotonicity for continuous-time Markov processes

\mathcal{A}

Supercritical probabilistic cellular automata: how effective is the synchronous updating?

). 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

Effective Parallelism Rate by Reversible PCA Dynamics

\{-1;+1\}^{\mathbb{Z}^d}

Increasing coupling of probabilistic cellular automata

with a naturally associated Gibbsian potential

Syncronization and functional central limit theorems for interacting reinforced random walks

\varphi

Synchronization in Interacting Reinforced Stochastic Processes

, we prove that a (spatial-) weak mixing condition (