# Complex projective metrics on Young towers, countable sub-shifts and other countable covering maps

## TL;DR

This paper develops a framework using complex projective metrics to analyze transfer operators associated with countable dynamical systems, leading to new probabilistic limit theorems for non-stationary processes.

## Contribution

It introduces a sequential Ruelle-Perron-Frobenius theorem for complex operators on countable systems, extending classical results to non-stationary and time-dependent maps.

## Key findings

- Established a new spectral gap result for complex transfer operators.
- Derived probabilistic limit theorems beyond the CLT for non-stationary processes.
- Applied the theory to Young towers and countable shifts.

## Abstract

In this article we will apply complex projective metrics to sequences of complex transfer operators generated by Young towers, countable shifts and other types of distance expanding maps (possibly time dependent) with countable degrees. We will derive a sequential Ruelle-Perron-Frobenius theorem for sequence of complex operators defined by such maps, and relying on it a variety of probabilistic limit theorems (finer than the CLT) for non-stationary processes follows.