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Stationary measures and phase transition for a class of probabilistic cellular automata
Paolo Dai Pra, Pierre-Yves Louis, Sylvie Roelly
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 transiti…
Ergodicity of PCA: Equivalence between Spatial and Temporal Mixing Conditions
Pierre-Yves Louis
For a general attractive Probabilistic Cellular Automata on S Z d , we prove that the (time-) convergence towards equilibrium of this Markovian parallel dynamics, exponentially fas…
Realizable monotonicity for continuous-time Markov processes
Paolo Dai Pra, Pierre-Yves Louis, Ida Minelli
We formalize and analyze the notions of stochastic monotonicity and realizable mono-tonicity for Markov Chains in continuous-time, taking values in a finite partially ordered set.…
Monotonicity and complete monotonicity for continuous-time Markov chains
Paolo Dai Pra, Pierre-Yves Louis, Ida Minelli
We analyze the notions of monotonicity and complete monotonicity for Markov Chains in continuous-time, taking values in a finite partially ordered set. Similarly to what happens in…
Synchronization via interacting reinforcement
Paolo Dai Pra, Pierre-Yves Louis, Ida G. Minelli
We consider a system of urns of Polya-type, with balls of two colors; the reinforcement of each urn depends both on the content of the same urn and on the average content of all ur…