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.
Article PDF
Similar content being viewed by others
Author information
Authors and Affiliations
Additional information
Received: 20 September 2001 / Revised version: 16 January 2002 / Published online: 22 August 2002
Rights and permissions
About this article
Cite this article
Bardet, JB. Limit theorems for coupled analytic maps. Probab Theory Relat Fields 124, 151–177 (2002). https://doi.org/10.1007/s004400200206
Issue Date:
DOI: https://doi.org/10.1007/s004400200206