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

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- by D. Dragičević, G. Froyland, C. González-Tokman and S. Vaienti PDF
- Trans. Amer. Math. Soc.
**373**(2020), 629-664 Request permission

## 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
- MR Author ID: 601207
- 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
- MR Author ID: 176525
- Email: vaienti@cpt.univ-mrs.fr
- 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 - © Copyright 2019 American Mathematical Society
- Journal: Trans. Amer. Math. Soc.
**373**(2020), 629-664 - MSC (2010): Primary 37D20, 60F05
- DOI: https://doi.org/10.1090/tran/7943
- MathSciNet review: 4042887