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The Kemeny Constant For Finite Homogeneous Ergodic Markov Chains

Catral, M. and Kirkland, S.J. and Neumann, M. and Sze, N.-S. (2010) The Kemeny Constant For Finite Homogeneous Ergodic Markov Chains. Journal of Scientific Computing, 45 (1-3). pp. 151-166. ISSN 0885-7474

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Abstract

A quantity known as the Kemeny constant, which is used to measure the expected number of links that a surfer on the World Wide Web, located on a random web page, needs to follow before reaching his/her desired location, coincides with the more well known notion of the expected time to mixing, i.e., to reaching stationarity of an ergodic Markov chain. In this paper we present a new formula for the Kemeny constant and we develop several perturbation results for the constant, including conditions under which it is a convex function. Finally, for chains whose transition matrix has a certain directed graph structure we show that the Kemeny constant is dependent only on the common length of the cycles and the total number of vertices and not on the specific transition probabilities of the chain.

Item Type: Article
Additional Information: The original publication is available at www.springerlink.com
Keywords: Nonnegative matrices; group inverses; directed graphs; Markov chains; stationary distribution vectors; stochastic matrices; mean first passage times;
Subjects: Science & Engineering > Hamilton Institute
Item ID: 2185
Depositing User: Professor Steve Kirkland
Date Deposited: 13 Oct 2010 15:31
Journal or Publication Title: Journal of Scientific Computing
Publisher: Springer Verlag
Refereed: No
URI:

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