Restoration of Gibbsianness for projected and FKG renormalized measures
type: Item
instance of: scholarly article
title: Restoration of Gibbsianness for projected and FKG renormalized measures
zbMATH Open document ID: 1055.60043
author: Roberto Fernandez
author: Arnaud Le Ny
author: F. Redig
published in: Bulletin of the Brazilian Mathematical Society. New Series
publication date: 2004-09-22T00:00:00Z
review text: The variational approach for almost quasilocal measures is studied. The authors establish conditions for the validity of the usual (specification-dependent) variational principle when a zero relative entropy density implies consistency with the same specification. The main theorem relates this implication to concentration properties of finite-volume relative densities. In order to apply this result the authors consider specifications that are monotonicity preserving in FKG sense and show that implications of the theorem regarding the almost quasilocality of the consistent measures. In the next application the monotonicity condition is replaced by the existence of appropriate ``continuity rates''. In particular, it is obtained that for projections to a line ``zero entropy density implies consistency with the same specification'' without any support assumption.
Mathematics Subject Classification ID: 60G60
Mathematics Subject Classification ID: 82B20
Mathematics Subject Classification ID: 82B30
zbMATH DE Number: 2101599
zbMATH Keywords: Gibbs measure
zbMATH Keywords: almost quasilocality
zbMATH Keywords: consistent measures
reviewed by: U. A. Rozikov
MaRDI profile type: Publication
full work available at URL: s00574-003-0023-2
OpenAlex ID: W2047067716
Wikidata QID: Q113107559
DOI: 10.1007/S00574-003-0023-2
description: scientific article; zbMATH DE number 2101599