%0 Journal Article %1 bini2017kemenys %A Bini, Dario %A Hunter, Jeffrey J. %A Latouche, Guy %A Meini, Beatrice %A Taylor, Peter G. %D 2017 %K birth-death-process markov-chain %T Why is Kemeny's constant a constant? %U http://arxiv.org/abs/1711.03313 %X 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.

@article{bini2017kemenys, 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.}, added-at = {2017-11-10T18:57:18.000+0100}, author = {Bini, Dario and Hunter, Jeffrey J. and Latouche, Guy and Meini, Beatrice and Taylor, Peter G.}, biburl = {https://www.bibsonomy.org/bibtex/2c5d100ffd3d4bb3837143ab518d9b602/claired}, description = {Why is Kemeny's constant a constant?}, interhash = {cbc0f1880c0a4a5bbd82bd2b11f1160f}, intrahash = {c5d100ffd3d4bb3837143ab518d9b602}, keywords = {birth-death-process markov-chain}, note = {cite arxiv:1711.03313}, timestamp = {2017-11-10T18:57:18.000+0100}, title = {Why is Kemeny's constant a constant?}, url = {http://arxiv.org/abs/1711.03313}, year = 2017 }