## Regenerative representation for one-dimensional Gibbs states.(English)Zbl 0612.60093

Dynamical systems determined by a stationary Gibbs state on $$\Omega =\{1,...,m\}^{{\mathbb{R}}}$$ and the forward shift are isomorphic to a Bernoulli shift. The coding for the isomorphism depends on the infinite past and future. The main result of this paper states that a Gibbs process may always be obtained by stringing together i.i.d. words of symbols from the underlying alphabet, with the word length having finite exponential moments.
Reviewer: U.Krengel

### MSC:

 60K35 Interacting random processes; statistical mechanics type models; percolation theory 60G10 Stationary stochastic processes 28D20 Entropy and other invariants

### Keywords:

stationary Gibbs state; Bernoulli shift; coding; Gibbs process
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