Please use this identifier to cite or link to this item: http://hdl.handle.net/10397/25636
Title: The Kemeny constant for finite homogeneous ergodic Markov chains
Authors: Catral, M
Kirkland, SJ
Neumann, M
Sze, NS 
Keywords: Directed graphs
Group inverses
Markov chains
Mean first passage times
Nonnegative matrices
Stationary distribution vectors
Stochastic matrices
Issue Date: 2010
Publisher: Springer
Source: Journal of scientific computing, 2010, v. 45, no. 1-3, p. 151-166 How to cite?
Journal: Journal of scientific computing 
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.
URI: http://hdl.handle.net/10397/25636
ISSN: 0885-7474
DOI: 10.1007/s10915-010-9382-1
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