Transformations of Gibbs states
This note contains the general results of the recent work [3]. There, in the axiomatic framework of Gibbs states P (developed in [4]) specified locally by some specification Pi. (sce 1.1), a class of transformations (phi, psi) is isolated which enables us to transform a very large class of specifications IT into a renormalized specification Pi (phi,psi) in such a way that the image P-phi of P under phi remains a Gibbs state, now specified by Pi (phi,psi). This result is an adaptation of Dynkin's theorem on state-space transformations of Markov processes [1]. Some corollaries show how one can transform Gibbs states on spaces of equivalence classes or on traversals of cross sections. Furthermore, local conditioning is discussed. Concrete applications and the proofs of these results can be found in [2,3]. (C) 2001 Academie des sciences/Editions scientifiques et medicales Elsevier SAS.
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