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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

A spectral approach for quenched limit theorems for random hyperbolic dynamical systems


Authors: D. Dragičević, G. Froyland, C. González-Tokman and S. Vaienti
Journal: Trans. Amer. Math. Soc. 373 (2020), 629-664
MSC (2010): Primary 37D20, 60F05
DOI: https://doi.org/10.1090/tran/7943
Published electronically: September 12, 2019
MathSciNet review: 4042887
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Abstract | References | Similar Articles | Additional Information

Abstract: We extend the recent spectral approach for quenched limit theorems developed for piecewise expanding dynamics under general random driving to quenched random piecewise hyperbolic dynamics.

For general ergodic sequences of maps in a neighborhood of a hyperbolic map we prove a quenched large deviations principle (LDP), central limit theorem (CLT), and local central limit theorem (LCLT).


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Additional Information

D. Dragičević
Affiliation: Department of Mathematics, University of Rijeka, 51000, Rijeka, Croatia
Email: ddragicevic@math.uniri.hr

G. Froyland
Affiliation: School of Mathematics and Statistics, University of New South Wales, Sydney, New South Wales 2052, Australia
Email: G.Froyland@unsw.edu.au

C. González-Tokman
Affiliation: School of Mathematics and Physics, The University of Queensland, St Lucia, Queensland 4072, Australia
Email: cecilia.gt@uq.edu.au

S. Vaienti
Affiliation: Aix Marseille Université, Université de Toulon, CNRS, CPT, 13009 Marseille, France
Email: vaienti@cpt.univ-mrs.fr

DOI: https://doi.org/10.1090/tran/7943
Received by editor(s): December 10, 2018
Received by editor(s) in revised form: April 29, 2019, May 2, 2019, July 2, 2019, and July 5, 2019
Published electronically: September 12, 2019
Additional Notes: The first author was supported by the Croatian Science Foundation under the project IP-2014-09-2285 and by the University of Rijeka under the project number uniri-prirod-18-9
The second and third authors thank AMU, CPT, and CIRM (Marseille) for hospitality during this research
The second author was partially supported by an ARC Discovery project
The third author was supported by an ARC DECRA
The fourth author was supported by the MATH AM-Sud Project Physeco and by the project APEX Systèmes dynamiques: Probabilitès et Approximation Diophantienne PAD funded by the Région PACA (France). The fourth author warmly thanks the LabEx Archiméde (AMU University, Marseille), the Laboratoire International Associé LIA LYSM, the INdAM (Italy), and the UMI-CNRS 3483, Laboratoire Fibonacci (Pisa), where this work was completed under a CNRS delegation
Article copyright: © Copyright 2019 American Mathematical Society