Spatio-temporal large deviations principle for coupled circle maps

Jean Baptiste Bardet, Gérard Ben Arous

Research output: Contribution to journalArticle

Abstract

We consider the (d +1)-dimensional an dynamical system constituted by weakly coupled expanding circle maps on ℤd 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 [Preprint (2002)] for such systems.

Original languageEnglish (US)
Pages (from-to)692-729
Number of pages38
JournalAnnals of Probability
Volume32
Issue number1 B
StatePublished - Jan 2004

Fingerprint

Circle Map
Coupled Maps
Large Deviation Principle
Dynamical system
Thermodynamic Formalism
Expanding Maps
Empirical Measures
Lebesgue Measure
Lemma
Ball
Coding
Orbit
Asymptotic Behavior
Dynamical systems
Large deviations
Thermodynamics
Asymptotic behavior
Formalism

Keywords

  • Coupled map lattices
  • Large deviations
  • Thermodynamic formalism

ASJC Scopus subject areas

  • Mathematics(all)
  • Statistics and Probability

Cite this

Spatio-temporal large deviations principle for coupled circle maps. / Bardet, Jean Baptiste; Arous, Gérard Ben.

In: Annals of Probability, Vol. 32, No. 1 B, 01.2004, p. 692-729.

Research output: Contribution to journalArticle

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