主讲人：Professor Jeffrey J Hunter, Auckland University of Technology, New Zealand 
    　时　间：2013年9月9日（周一）13:30
　　地　点：格致中楼503
 
　　报告内容摘要：
　　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, thatΣmπj =1 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.
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