The Kemeny constant of a Markov chain - Mathematics > ProbabilityReport as inadecuate

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Abstract: Given an ergodic finite-state Markov chain, let M {iw} denote the mean timefrom i to equilibrium, meaning the expected time, starting from i, to arrive ata state selected randomly according to the equilibrium measure w of the chain.John Kemeny observed that M {iw} does not depend on starting the point i. Thecommon value K=M {iw} is the Kemeny constant or seek time of the chain. K is aspectral invariant, to wit, the trace of the resolvent matrix. We review basicfacts about the seek time, and connect it to the bus paradox and the CentralLimit Theorem for ergodic Markov chains.

Author: Peter G. Doyle


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