Regenerative representation for one-dimensional Gibbs states (Q1088310)

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.