  We observe that the technique of Markov contraction can be used to establish
measure concentration for a broad class of non-contracting chains. In
particular, geometric ergodicity provides a simple and versatile framework.
This leads to a short, elementary proof of a general concentration inequality
for Markov and hidden Markov chains (HMM), which supercedes some of the known
results and easily extends to other processes such as Markov trees. As
applications, we give a Dvoretzky-Kiefer-Wolfowitz-type inequality and a
uniform Chernoff bound. All of our bounds are dimension-free and hold for
countably infinite state spaces.
