Abstract
In their 1960 book on finite Markov chains, Kemeny and Snell established that
a certain sum is invariant. 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 denumerably
infinite state space, the physical argument holds but the constant may be
infinite. We consider the special case of birth-and-death processes and
determine the condition for Kemeny's constant to be finite.
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