Probability Theory and Related Fields

, Volume 124, Issue 2, pp 151–177 | Cite as

Limit theorems for coupled analytic maps

  • Jean-Baptiste Bardet

Abstract.

 In [23], H.H. Rugh gave a new and simpler method to prove existence of an invariant measure with nice mixing properties for some weakly coupled analytic maps. He proved in fact a spectral gap property for a well-defined transfer operator. We modify this method to construct generalized transfer operators associated to potentials and preserve the spectral gap for small potentials. This allows us to prove new limit results for these systems: Central Limit Theorem, Moderate Deviations Principle and a partial Large Deviations result. These results are available under wide classes of observables and initial measures.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Jean-Baptiste Bardet
    • 1
  1. 1.Département de Mathématiques, Ecole Polytechnique Fédérale de Lausanne, 1015 Lausanne, Switzerland. e-mail: Jean-Baptiste.Bardet@epfl.chCH

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