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

## TL;DR

This paper extends spectral methods to establish quenched limit theorems, including LDP, CLT, and LCLT, for random hyperbolic dynamical systems such as billiards, broadening the scope beyond previous piecewise expanding cases.

## Contribution

It introduces a spectral approach for quenched limit theorems applicable to random hyperbolic systems, including billiards, under general ergodic sequences of maps.

## Key findings

- Proved quenched large deviations principle for hyperbolic systems.
- Established quenched central limit theorem in this setting.
- Derived local central limit theorem for random hyperbolic dynamics.

## Abstract

We extend the recent spectral approach for quenched limit theorems developed for piecewise expanding dynamics under general random driving [DrFrGTVa18] to quenched random piecewise hyperbolic dynamics including some classes of billiards. For general ergodic sequences of maps in a neighbourhood of a hyperbolic map we prove a quenched large deviations principle (LDP), central limit theorem (CLT), and local central limit theorem (LCLT).