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Article Dans Une Revue Stochastic Processes and their Applications Année : 2011

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

Résumé

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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Dates et versions

hal-00512864 , version 1 (31-08-2010)
hal-00512864 , version 2 (11-10-2010)
hal-00512864 , version 3 (08-07-2011)

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Philippe Chassaing, Jean Mairesse. A non-ergodic probabilistic cellular automaton with a unique invariant measure. Stochastic Processes and their Applications, 2011, 121 (11), pp.2474-2487. ⟨10.1016/j.spa.2011.06.009⟩. ⟨hal-00512864v3⟩
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