Richard Wilkinson
Professor Jeff Hunter (Aukland University of Technology)
Abstract
"The Role of Kemeny's Constant in Properties of Markov Chains"
Professor Jeffrey J Hunter
Auckland University of Technology
New Zealand
In a finite m-state irreducible Markov chain with stationary probabilities {πi} and mean first passage times mij (mean recurrence time when i = j) it was first shown, by Kemeny and Snell, that π j =1 j m Σ mij is a constant, K, not depending on i. This constant has since become known as Kemeny’s constant. We consider a variety of techniques for finding expressions for K, derive some bounds for K, and explore various applications and interpretations of these results. Interpretations include the expected number of links that a surfer on the World Wide Web located on a random page needs to follow before reaching a desired location, as well as the expected time to mixing in a Markov chain. Various applications have been considered including some perturbation results, mixing on directed graphs and its relation to the Kirchhoff index of regular graphs.
The University of NottinghamUniversity Park Nottingham, NG7 2RD
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