The optimal sink and the best source in a Markov chain - Mathematics > ProbabilityReport as inadecuate




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Abstract: It is well known that the distributions of hitting times in Markov chains arequite irregular, unless the limit as time tends to infinity is considered. Weshow that nevertheless for a typical finite irreducible Markov chain and fornondegenerate initial distributions the tails of the distributions of thehitting times for the states of a Markov chain can be ordered, i.e., they donot overlap after a certain finite moment of time.If one considers instead each state of a Markov chain as a source rather thana sink then again the states can generically be ordered according to theirefficiency. The mechanisms underlying these two orderings are essentiallydifferent though.



Author: Yuri Bakhtin, Leonid Bunimovich

Source: https://arxiv.org/







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