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

   
@article{EJP3189,
	author = {Jean-René Chazottes and Frank Redig},
	title = {Thermodynamic formalism and large deviations for multiplication-invariant potentials on lattice spin systems},
	journal = {Electron. J. Probab.},
	fjournal = {Electronic Journal of Probability},
	volume = {19},
	year = {2014},
	keywords = {},
	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.},
	pages = {no. 39, 1-19},
	issn = {1083-6489},
	doi = {10.1214/EJP.v19-3189},    
        url = {http://ejp.ejpecp.org/article/view/3189}}