Variational principle and almost quasilocality for some renormalized measures
Probability
2007-05-23 v1 Mathematical Physics
math.MP
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 energies 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 and for models with appropriate "continuity rates". For (noisy) decimations or projections of the Ising model, these results imply almost quasilocality of the decimated "+" and "-" measures.
Cite
@article{arxiv.math/0107081,
title = {Variational principle and almost quasilocality for some renormalized measures},
author = {Roberto Fernandez and Arnaud Le Ny and Frank Redig},
journal= {arXiv preprint arXiv:math/0107081},
year = {2007}
}
Comments
19 pages, LaTeX