Concentration inequalities and rates of convergence of the ergodic theorem for countable shifts with Gibbs measures

Abstract

In this paper we obtain an exponential concentration inequality for a countable Markov shift with a Gibbs measure associated to a Hölder continuous potential ϕ. We apply concentration inequalities to obtain bounds on the rate of convergence of the ergodic theorem for Lipschitz observables and for the wider class of bounded and -a.e. continuous observables.