A structured condition number for Kemeny's constant
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Date
2019
Authors
Breen, Jane
Kirkland, Steve
Journal Title
Journal ISSN
Volume Title
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