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2014 Thermodynamic formalism and large deviations for multiplication-invariant potentials on lattice spin systems
Jean-René Chazottes, Frank Redig
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Electron. J. Probab. 19: 1-19 (2014). DOI: 10.1214/EJP.v19-3189

Abstract

We introduce the multiplicative Ising model and prove basic properties of its thermodynamic formalism such as existence of pressure and entropies. We generalize to one-dimensional "layer-unique'' Gibbs measures for which the same results can be obtained. For more general models associated to a $d$-dimensional multiplicative invariant potential, we prove a large deviation theorem in the uniqueness regime for averages of multiplicative shifts of general local functions. This thermodynamic formalism is motivated by the statistical properties of multiple ergodic averages.

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Jean-René Chazottes. Frank Redig. "Thermodynamic formalism and large deviations for multiplication-invariant potentials on lattice spin systems." Electron. J. Probab. 19 1 - 19, 2014. https://doi.org/10.1214/EJP.v19-3189

Information

Accepted: 1 April 2014; Published: 2014
First available in Project Euclid: 4 June 2016

zbMATH: 1290.82004
MathSciNet: MR3194738
Digital Object Identifier: 10.1214/EJP.v19-3189

Subjects:
Primary: 60K35
Secondary: 60F10

JOURNAL ARTICLE
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Vol.19 • 2014
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