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 1 2004

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Keywords

  • Coupled map lattices
  • Large deviations
  • Thermodynamic formalism

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

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