A class of non-ergodic probabilistic cellular automata with unique invariant measure and quasi-periodic orbit

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:125

Article

Jahnel, Benedikt¹  Kuelske, Christof¹ 

[1] Ruhr Univ Bochum, Fak Math, D-44801 Bochum, Germany

关键词: Markov chain;    Probabilistic cellular automaton;    Interacting particle system;    Non-equilibrium;    Nonergodicity;    Rotation;    Discretization;    Gibbs measures;    XY-model;    Clock model;   

DOI  :  10.1016/j.spa.2015.01.006

来源: Elsevier

【 摘 要 】

We provide an example of a discrete-time Markov process on the three-dimensional infinite integer lattice with Z(q)-invariant Bernoulli-increments which has as local state space the cyclic group Z(q). We show that the system has a unique invariant measure, but remarkably possesses an invariant set of measures on which the dynamics is conjugate to an irrational rotation on the continuous sphere S-1. The update mechanism we construct is exponentially well localized on the lattice. (C) 2015 Elsevier B.V. All rights reserved.

【 授权许可】

Free