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We introduce a novel time-homogeneous Markov embedding of a class of timeinhomogeneous Markov chains widely used in the context of Monte Carlo samplingalgorithms which allows us to answer one of the most basic, yet hard, questionabout the practical implementation of these techniques. We also show that thisembedding sheds some light on the recent result of [#maire-douc-olsson2013]. Wediscuss further applications of the technique.

A note on one of the Markov chain Monte Carlo novice's questions