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

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:121

Article

Chassaing, Philippe³  Mairesse, Jean^1,2 

[1] CNRS, LIAFA, F-75205 Paris 13, France

[2] Univ Paris 07, F-75205 Paris 13, France

[3] Univ Henri Poincare, Inst Elie Cartan, F-54506 Vandoeuvre Les Nancy, France

关键词: Probabilistic cellular automaton;    Interacting particle system;    Ergodicity;   

DOI  :  10.1016/j.spa.2011.06.009

来源: Elsevier

【 摘 要 】

We exhibit a Probabilistic Cellular Automaton (PCA) on {0, 1}(Z) with 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. (C) 2011 Elsevier B.V. All rights reserved.

【 授权许可】

Free