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  • Faculty of Design and Creative Technologies (Te Ara Auaha)
  • School of Engineering, Computer and Mathematical Sciences - Te Kura Mātai Pūhanga, Rorohiko, Pāngarau
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The distribution of Mixing Times in Markov Chains

Hunter, JJ
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http://hdl.handle.net/10292/4810
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Abstract
The distribution of the “mixing time” or the “time to stationarity” in a discrete time irreducible Markov chain, starting in state i, can be defined as the number of trials to reach a state sampled from the stationary distribution of the Markov chain. Expressions for the probability generating function, and hence the probability distribution of the mixing time, starting in state i, are derived and special cases explored. This extends the results of the author regarding the expected time to mixing [Hunter, J J (2006). Mixing times with applications to perturbed Markov chains. Linear Algebra and its Applications, 417, 108-123] and the variance of the times to mixing, [Hunter, J J (2008). Variances of First Passage Times in a Markov chain with applications to Mixing Times. Linear Algebra and its Applications, 429, 1135-1162]. Some new results for the distribution of the recurrence and the first passage times in a general irreducible three-state Markov chain are also presented.
Keywords
Markov chains; Stationary distribution; Frst passage times; Hitting times; Mixing times; Time to stationarity; Kemeny constant; Distributions
Date
2012
Source
Asia - Pacific Journal of Operational Research, vol.30(1)
Item Type
Journal Article
Publisher
World Scientific Publishing Co & Operational Research Society of Singapore
DOI
10.1142/S0217595912500455
Publisher's Version
http://dx.doi.org/10.1142/S0217595912500455
Rights Statement
Electronic version of an article published as (please see citation) [Article DOI] © copyright World Scientific Publishing Company (please see Publisher’s Version).

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