Positive-rate probabilistic cellular automata admitting stationary Bernoulli measures are exponentially ergodic with logarithmic mixing times for finite regions.
K˚ urka.Topological and Symbolic Dynamics, volume 11 ofCours Sp´ ecialis´ es
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Positive-rate PCA and IPS with stationary Bernoulli measures are rapidly forgetful
Positive-rate probabilistic cellular automata admitting stationary Bernoulli measures are exponentially ergodic with logarithmic mixing times for finite regions.