Spatio-temporal large deviations principle for coupled circle maps

• 成果类型: Article
• 署名作者: Bardet, JB; Ben Arous, GR
• 署名单位: Universite Paris Nanterre; Swiss Federal Institutes of Technology Domain; Ecole Polytechnique Federale de Lausanne
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• 发表日期: 2004
• 页码: 692-729
• 关键词: pointwise theorems; gibbs; expansiveness; FORMULA

摘要

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 [Preprint (2002)] for such systems.