Why is Kemeny's constant a constant?
Dario Bini, Jeffrey J Hunter, Guy Latouche, Beatrice Meini, Peter Taylor
Journal of Applied Probability | Cambridge University Press | Published : 2018
In their 1960 book on finite Markov chains, Kemeny and Snell established that a certain sum is invariant. The value of this sum has become known as Kemeny’s constant. Various proofs have been given over time, some more technical than others. We give here a very simple physical justification, which extends without a hitch to continuous-time Markov chains on a finite state space. For Markov chains with denumerably infinite state space, the constant may be infinite and even if it is finite, there is no guarantee that the physical argument will hold. We show that the physical interpretation does go through for the special case of a birth-and-death process with a finite value of Kemeny’s constant..View full abstract
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Awarded by Australian Research Council (ARC) Laureate Fellowship
P.G. Taylor's research is supported by the Australian Research Council (ARC) Laureate Fellowship FL130100039 and the ARC Centre of Excellence for the Mathematical and Statistical Frontiers (ACEMS).