Gibbs states and Gibbsian specifications on the space R~N

摘要

We are interested in the study of Gibbs and equilibrium probabilities on the space state R~N. We consider the unilateral full-shift a defined on the non-compact set R~N, that is σ(x_1x_2, ..,x_n,..) = (x_2,X_3, ..,x_n,..), and a Holder continuous potential A : R~N → R. From a suitable class of a priori probability measures v 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 R~N and we show that this family of probabilities satisfies a FKG-inequality.