# The Optimal Sink and the Best Source in a Markov Chain

@article{Bakhtin2011TheOS,
title={The Optimal Sink and the Best Source in a Markov Chain},
author={Yuri Bakhtin and Leonid A. Bunimovich},
journal={Journal of Statistical Physics},
year={2011},
volume={143},
pages={943-954}
}
• Published 13 July 2010
• Mathematics
• Journal of Statistical Physics
It is well known that the distributions of hitting times in Markov chains are quite irregular, unless the limit as time tends to infinity is considered. We show that nevertheless for a typical finite irreducible Markov chain and for nondegenerate initial distributions the tails of the distributions of the hitting times for the states of a Markov chain can be ordered, i.e., they do not overlap after a certain finite moment of time. If one considers instead each state of a Markov chain as a…
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