Geodesic
Absolute continuity between a Gibbs measure
Teoriâ veroâtnostej i ee primeneniâ, Tome 49 (2004) no. 4, pp. 816-826

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We look for an overestimation of the distance in total variation between a Gibbs measure on $R^{Z^d}$ and its translate by a vector of this space. This can be done thanks to a control of the interdependence between the spins at distinct sites, i.e., prescribing some restrictions for the associated potential. We can then conclude, for precise cases, with the equivalence of the initial measure and its translate.
Keywords: random fields, Gibbs measures, equivalence of measures.
Mots-clés : distance in total variation 
@article{TVP_2004_49_4_a14,
     author = {E. Nowak},
     title = {Absolute continuity between a {Gibbs} measure},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {816--826},
     publisher = {mathdoc},
     volume = {49},
     number = {4},
     year = {2004},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_2004_49_4_a14/}
}
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E. Nowak. Absolute continuity between a Gibbs measure. Teoriâ veroâtnostej i ee primeneniâ, Tome 49 (2004) no. 4, pp. 816-826. http://geodesic.mathdoc.fr/item/TVP_2004_49_4_a14/