# A quantitative Mc Diarmid's inequality for geometrically ergodic Markov chains

## TL;DR

This paper develops a quantitative version of Mc Diarmid's inequality tailored for geometrically ergodic Markov chains, enhancing the understanding of concentration inequalities in dependent stochastic processes.

## Contribution

It introduces a modified coupling argument to extend the bounded difference inequality to all geometrically ergodic Markov chains, filling a gap in existing methods.

## Key findings

- Provides a new quantitative bound for Markov chains
- Extends Mc Diarmid's inequality to a broader class of chains
- Improves the theoretical tools for analyzing dependent data

## Abstract

We state and prove a quantitative version of the bounded difference inequality for geometrically ergodic Markov chains. Our proof uses the same martingale decomposition as \cite{MR3407208} but, compared to this paper, the exact coupling argument is modified to fill a gap between the strongly aperiodic case and the general aperiodic case.