Ergodicity of Noisy Cellular Automata: The Coupling Method and Beyond

摘要

When perturbating a cellular automaton by a random noise (positive probability of error, for each cell independently), the system is generally expected to be ergodic, meaning that during its evolution, it eventually forgets about its initial condition. For a high noise, this can be shown by coupling. However, for a small noise, ergodicity is often very difficult to prove. We present extensions of the coupling method to small noises when the cellular automaton has some specific properties (hardcore exclusion, nilpotency, permutivity).