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