On uniform closeness of local times of Markov chains and i.i.d.   sequences
  In this paper we consider the field of local times of a discrete-time Markov chain on a general state space, and obtain uniform (in time) upper bounds on the total variation distance between this field and the one of a sequence of $n$ i.i.d. random variables with law given by the invariant measure of that Markov chain. The proof of this result uses a refinement of the soft local time method of [11]. 
Diego F. de Bernardini, Christophe Gallesco, Serguei Popov
math.PR