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

Lalley, S. P.

Ann. Probab. 14, 1262-1271 (1986).

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