The Annals of Probability

Spatio-temporal large deviations principle for coupled circle maps

Jean-Baptiste Bardet and Gérard Ben Arous

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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.

Article information

Source
Ann. Probab. Volume 32, Number 1B (2004), 692-729.

Dates
First available: 11 March 2004

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

Subjects
Primary: 60F10: Large deviations 37A50: Relations with probability theory and stochastic processes [See also 60Fxx and 60G10] 37L60: Lattice dynamics [See also 37K60]

Keywords
Coupled map lattices large deviations thermodynamic formalism

Citation

Bardet, Jean-Baptiste; Ben Arous, Gérard. Spatio-temporal large deviations principle for coupled circle maps. The Annals of Probability 32 (2004), no. 1B, 692--729. doi:10.1214/aop/1079021461. http://projecteuclid.org/euclid.aop/1079021461.


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