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Limit theorems for coupled analytic maps
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  • Published: October 2002

Limit theorems for coupled analytic maps

  • Jean-Baptiste Bardet1 

Probability Theory and Related Fields volume 124, pages 151–177 (2002)Cite this article

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

    Jean-Baptiste Bardet

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  1. Jean-Baptiste Bardet
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Received: 20 September 2001 / Revised version: 16 January 2002 / Published online: 22 August 2002

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Bardet, JB. Limit theorems for coupled analytic maps. Probab Theory Relat Fields 124, 151–177 (2002). https://doi.org/10.1007/s004400200206

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  • Issue Date: October 2002

  • DOI: https://doi.org/10.1007/s004400200206

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Keywords

  • Generalize Transfer
  • Limit Theorem
  • Invariant Measure
  • Central Limit
  • Central Limit Theorem
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