Abstract
We are interested in the study of Gibbs and equilibrium probabilities on the space state . We consider the unilateral full-shift σ defined on the non-compact set , that is , and a Hölder continuous potential . From a suitable class of a priori probability measures ν we define the Ruelle operator associated to A and we show the existence of eigenfunctions, conformal probability measures and equilibrium states associated to A. Moreover, we prove the existence of an involution kernel for A, we build a Gibbsian specification for the Borelian sets on and we show that this family of probabilities satisfies a FKG-inequality.
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