Path Large Deviation and Other Typical Properties of the Low-Temperature Models, with Applications to the Weakly Gibbs States

S. Shlosman

2000, v.6, Issue 2, 121-133


We establish a new property of typical configurations of the low temperature pure phases, which we call the Amoeba Property. This property is less restrictive than the Path Large Deviation property, introduced in [C. Maes, F. Redig, S. Shlosman and A. van Moffaert, Percolation, path large deviations and Weakly Gibbs States, Commun. Math. Phys., 2000]. It allows us to extend the range of the validity of the Weakly Gibbs property of random fields. Namely, we prove that the marginals of Gibbs fields are Weakly Gibbs fields.

Keywords: large deviations,typical property,weakly Gibbs state,quenched correlationdecay


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