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

Published 1 Sep 2010 in cs.FL, cs.DM, and math.PR | (1009.0143v3)

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.

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