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January 2004 Spatio-temporal large deviations principle for coupled circle maps
Jean-Baptiste Bardet, Gérard Ben Arous
Ann. Probab. 32(1B): 692-729 (January 2004). DOI: 10.1214/aop/1079021461


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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Jean-Baptiste Bardet. Gérard Ben Arous. "Spatio-temporal large deviations principle for coupled circle maps." Ann. Probab. 32 (1B) 692 - 729, January 2004.


Published: January 2004
First available in Project Euclid: 11 March 2004

zbMATH: 1054.60032
MathSciNet: MR2039940
Digital Object Identifier: 10.1214/aop/1079021461

Primary: 37A50 , 37L60 , 60F10

Keywords: Coupled map lattices , large deviations , Thermodynamic formalism

Rights: Copyright © 2004 Institute of Mathematical Statistics


Vol.32 • No. 1B • January 2004
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