Increasing coupling of probabilistic cellular automata
Copyright policy )Increasing coupling of probabilistic cellular automata
We give a necessary and sufficient condition for the existence of an increasing coupling of $N$ ($N \geq 2$) synchronous dynamics on $S^{\mathbb Z^d}$(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 PCA's 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.
- HMU Potsdam – Health and Medical University Potsdam Germany
- Institut für Mathematik Germany
- University of Potsdam Germany
ddc:510, Stochastic ordering, [MATH.MATH-PR] Mathematics [math]/Probability [math.PR], Statistical Mechanics (cond-mat.stat-mech), Probability (math.PR), Institut für Mathematik, FOS: Physical sciences, Interacting random processes; statistical mechanics type models; percolation theory, Probabilistic Cellular Automata, Dynamic lattice systems (kinetic Ising, etc.) and systems on graphs in time-dependent statistical mechanics, stochastic ordering, monotone coupling, 60K35, 60E15, 60J10, 82C20, 37B15, 68W10, Markov chains (discrete-time Markov processes on discrete state spaces), Monotone Coupling, Dynamical aspects of cellular automata, FOS: Mathematics, Inequalities; stochastic orderings, Parallel algorithms in computer science, partially ordered spaces, Mathematics - Probability, Condensed Matter - Statistical Mechanics
ddc:510, Stochastic ordering, [MATH.MATH-PR] Mathematics [math]/Probability [math.PR], Statistical Mechanics (cond-mat.stat-mech), Probability (math.PR), Institut für Mathematik, FOS: Physical sciences, Interacting random processes; statistical mechanics type models; percolation theory, Probabilistic Cellular Automata, Dynamic lattice systems (kinetic Ising, etc.) and systems on graphs in time-dependent statistical mechanics, stochastic ordering, monotone coupling, 60K35, 60E15, 60J10, 82C20, 37B15, 68W10, Markov chains (discrete-time Markov processes on discrete state spaces), Monotone Coupling, Dynamical aspects of cellular automata, FOS: Mathematics, Inequalities; stochastic orderings, Parallel algorithms in computer science, partially ordered spaces, Mathematics - Probability, Condensed Matter - Statistical Mechanics
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