The Kemeny constant of a Markov chain

Details The Kemeny constant of a Markov chain The Kemeny constant of a Markov chain

2009-09-14

arxiv.org/abs/0909.2636v1

Mathematics

Probability

Version 1.0 dated 14 September 2009; GNU FDL

Scientific paper

Given an ergodic finite-state Markov chain, let M_{iw} denote the mean time from i to equilibrium, meaning the expected time, starting from i, to arrive at a 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. The common value K=M_{iw} is the Kemeny constant or seek time of the chain. K is a spectral invariant, to wit, the trace of the resolvent matrix. We review basic facts about the seek time, and connect it to the bus paradox and the Central Limit Theorem for ergodic Markov chains.

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