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Special Matrices

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CiteScore 2018: 0.64

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Why the Kemeny Time is a constant

Karl Gustafson / Jeffrey J. Hunter
  • Department of Mathematical Sciences, School of Engineering, Computer and Mathematical Sciences, Auckland University of Technology
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
Published Online: 2016-03-18 | DOI: https://doi.org/10.1515/spma-2016-0016


We present a new fundamental intuition forwhy the Kemeny feature of a Markov chain is a constant. This new perspective has interesting further implications.

Keywords: Markov chains; Mixing; Kemeny constant


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  • [2] I. Gialampoukidis, K. Gustafson, and I. Antoniou, Time operator ofMarkov chains and mixing times. Applications to financial data, Physica A 415(2014), 141-155. Google Scholar

  • [3] J.G Kemeny and J.L. Snell, Finite Markov Chains, Van Nostrand, Princeton, NJ, 1960. Google Scholar

  • [4] D. Lay, Linear Algebra and its Applications, 4th Ed., Addison Wesley, Boston, MA, 2012. Google Scholar

  • [5] J.J Hunter, Mathematical Techniques of Applied Probability, Volume 2, Discrete Time Models: Techniques and Application, Academic Press, New York, NY, 1983. Google Scholar

  • [6] R.A Horn, and C.R Johnson, Matrix Analysis, Cambridge University Press, Cambridge, UK, 1985. Google Scholar

  • [7] K. Gustafson, Antieigenvalue Analysis, with Applications to Numerical Analysis, Wavelets, Statistics, Quantum Mechanics, Finance and Optimization, World-Scientific, Singapore, 2012. Google Scholar

  • [8] I. Antoniou, Th. Christidis, and K.Gustafson, Probability from chaos, International J. of Quantum Chemistry 98 (2004) pp 150-159. Google Scholar

About the article

Received: 2015-09-30

Accepted: 2016-02-21

Published Online: 2016-03-18

Citation Information: Special Matrices, Volume 4, Issue 1, ISSN (Online) 2300-7451, DOI: https://doi.org/10.1515/spma-2016-0016.

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©2016 Karl Gustafson and Jeffrey J. Hunter. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License. BY-NC-ND 3.0

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Jeffrey J. Hunter
Linear Algebra and its Applications, 2018

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