# Weak Gibbs measures and large deviations

## TL;DR

This paper establishes large deviations estimates for weak Gibbs measures in dynamical systems, providing insights into the probability of deviations from typical behavior.

## Contribution

It introduces large deviations results specifically for weak Gibbs measures, extending the understanding of statistical properties in dynamical systems.

## Key findings

- Large deviations estimates are proved for weak Gibbs measures.
- The results apply to systems with weak Gibbs measures, broadening the scope of statistical analysis.
- The paper advances the theoretical framework connecting Gibbs measures and large deviations.

## Abstract

Let (X,T) be a dynamical system, where X is a compact metric space and T a continuous onto map. For weak Gibbs measures we prove large deviations estimates.