The optimal sink and the best source in a Markov chain

Details The optimal sink and the best source in a Markov chain The optimal sink and the best source in a Markov chain

2010-07-13

arxiv.org/abs/1007.2035v2

Journal of Statistical Physics: Volume 143, Issue 5 (2011), Page 943-954

Mathematics

Probability

12 pages, 1 figure

Scientific paper

10.1007/s10955-011-0223-x

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 source rather than a sink then again the states can generically be ordered according to their efficiency. The mechanisms underlying these two orderings are essentially different though.

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