A structured condition number for Kemeny's constant

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Date
2019
Authors
Breen, Jane
Kirkland, Steve
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Publisher
SIAM Journal on Matrix Analysis and Applications
Abstract
Kemeny's constant is an interesting and useful quantifier describing the global average behaviour of a Markov chain. In this article, we examine the sensitivity of Kemeny's constant to perturbations in the transition probabilities. That is, we consider the problem of generating a condition number for Kemeny's constant, to give an indication of the size of the change in its value relative to the size of the perturbation. We provide a structured condition number and determine some illuminating upper and lower bounds which connect the conditioning of Kemeny's constant to well-studied condition numbers for the stationary vector of the Markov chain. We also investigate the behaviour of this structured condition number for several infinite families of Markov chains.
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Keywords
Kemeny's constant, condition number, Markov chains, group inverse
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