2012/08/23 by Jeffrey J. Hunter · 89 citations
Mathematics · #Balance equation #Combinatorics #Computer science #Constant (computer programming) #Discrete mathematics #Examples of Markov chains #Generalization #Graph theory and applications #Limits and Structures in Graph Theory #Markov Chains and Monte Carlo Methods #Markov chain #Markov chain mixing time #Markov model #Mathematical analysis #Mathematics #Mixing (physics) #Physics #Statistics #math.PR #msc:60J10
paper · pdf · doi:10.1080/03610926.2012.741742
published in Communication in Statistics- Theory and Methods 43(7), 1309-1321 (Taylor & Francis) · 13 pages
arxiv created 2012/08/23 · openalex publication_date 2014/03/14 · arxiv updated 2014/03/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
In a finite irreducible Markov chain with stationary probabilities π i and mean first passage times m ij (mean recurrence time when i = j) it was first shown, by Kemeny and Snell (1960 Kemeny , J. G. , Snell , J. L. ( 1960 ). Finite Markov Chains . Princeton, NJ : Van Nostrand . Republished (1976) as Finite Markov Chains: With a New Appendix Generalization of a Fundamental Matrix. New York: Springer-Verlag . [Google Scholar]), that is a constant, K, (Kemeny's constant) not depending on i. A variety of techniques for finding expressions and bounds for K are given. The main interpretation focuses on its role as the expected time to mixing in a Markov chain. Various applications are considered including perturbation results, mixing on directed graphs and its relation to the Kirchhoff index of regular graphs.