A non-ergodic probabilistic cellular automaton with a unique invariant measure

Abstract

We exhibit a Probabilistic Cellular Automaton (PCA) on the integers with an alphabet and a neighborhood of size 2 which is non-ergodic although it has a unique invariant measure. This answers by the negative an old open question on whether uniqueness of the invariant measure implies ergodicity for a PCA.

To appear in Stochastic Processes and their Applications

References in corpus (1)

• Reliable Cellular Automata with Self-Organization

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