01-260 Roberto Fernandez, Arnaud Le Ny, Frank Redig.

Variational principle and almost quasilocality for some renormalized measures. (160K, postscript) Jul 11, 01

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Abstract. We restore part of the thermodynamic formalism for some renormalized measures that are known to be non-Gibbsian. We first point out that a recent theory due to Pfister implies that for block-transformed measures free energy and relative entropy densities exist and are conjugate convex functionals. We then determine a necessary and sufficient condition for consistency with a specification that is quasilocal in a fixed direction. As corollaries, we obtain consistency results for models with FKG monotonicity with appropriate "continuity rates". For (noisy) decimations or projections of the Ising model these results imply almost quasilocality of the decimated "+" and "-" measures.

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