On uniform closeness of local times of Markov chains and i.i.d. sequences

Abstract

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].

arXiv comment42 pages, 2 figures, coupling construction of Section 4 corrected, results unchanged

References in corpus (5)

• Soft local times and decoupling of random interlacements
• On large deviations for the cover time of two-dimensional torus
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Cited by in corpus (2)

• Two-dimensional Brownian random interlacements
• An improved decoupling inequality for random interlacements