Spatio-temporal large deviations principle for coupled circle maps

• Jean-Baptiste Bardet ^[1] ; Gérard Ben Arous ^[2]
  1. [1] Paris West University Nanterre La Défense

     Paris West University Nanterre La Défense

     París, Francia

     
  2. [2] Courant Institute and EPF - Lausane
• Localización: Annals of probability: An official journal of the Institute of Mathematical Statistics, ISSN 0091-1798, Vol. 32, Nº. 1, 2, 2004, págs. 692-729
• Idioma: inglés
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• Resumen

  • 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 for such systems.