### Thermodynamic formalism and large deviations for multiplication-invariant potentials on lattice spin systems

**Jean-René Chazottes**

*(CNRS & École Polytechnique)*

**Frank Redig**

*(Delft University of Technology)*

#### 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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Pages: 1-19

Publication Date: April 1, 2014

DOI: 10.1214/EJP.v19-3189

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