Large deviations for some unbounded observables in dynamical systems

TL;DR

This paper develops large deviations estimates for unbounded observables in dynamical systems, specifically for strongly mixing Markov chains and expanding maps, extending the understanding of probabilistic behavior in these systems.

Contribution

It introduces large deviations estimates for unbounded observables in dynamical systems, including Markov chains and expanding maps, which was not previously established.

Findings

Large deviations estimates for strongly mixing Markov chains in Lp norm

Application of estimates to locally constant random cocycles with mixed rank

Results for unbounded observables of expanding maps

Abstract

In this paper we establish a large deviations type estimate for strongly mixing Markov chains with respect to the Lp norm. As applications we derive such estimates for the iterates of a locally constant random cocycle with mixed rank, as well as for unbounded observables of expanding maps.