Spatio-temporal large deviations principle for coupled circle maps
Jean-Baptiste Bardet and Gérard Ben Arous
Source: Ann. Probab. Volume 32, Number 1B
(2004), 692-729.
Abstract
We consider the $(d+1)$-dimensional an dynamical system constituted by weakly coupled expanding circle maps on $\Z^d$ together with the spatial shifts. This viewpoint allows us to use thermodynamic formalism, and to describe the asymptotic behavior of the system in this setup. We obtain a volume lemma, which describes the exponential behavior of the size under Lebesgue measure of dynamical balls around any orbit, and then a large deviations principle for the empirical measure associated to this dynamical system. The proofs are direct: we do not use the coding constructed by Jiang for such systems.
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Permanent link to this document: http://projecteuclid.org/euclid.aop/1079021461
Digital Object Identifier: doi:10.1214/aop/1079021461
Mathematical Reviews number (MathSciNet): MR2039940
Zentralblatt MATH identifier: 02100731
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