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dc.contributor.authorHunter, JJ
dc.date.accessioned2012-01-19T22:07:38Z
dc.date.available2012-01-19T22:07:38Z
dc.date.copyright2011-11-01
dc.date.issued2012-01-20
dc.identifier.citationarXiv:1111.0151
dc.identifier.urihttp://hdl.handle.net/10292/3280
dc.description.abstractThe 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 [J.J. Hunter, Mixing times with applications to perturbed Markov chains, Linear Algebra Appl. 417 (2006) 108–123], and the variance of the times to mixing, [J.J. Hunter, Variances of first passage times in a Markov chain with applications to mixing times, Linear Algebra Appl. 429 (2008) 1135–1162]. Some new results for the distribution of recurrence and first passage times in three-state Markov chain are also presented.
dc.publisherarXiv
dc.relation.urihttp://arxiv.org/abs/1111.0151
dc.rightsarXiv does not ask that copyright be transferred. However, we require sufficient rights to allow us to distribute submitted articles in perpetuity. In order to submit an article to arXiv, the submitter must either: grant arXiv.org a non-exclusive and irrevocable license to distribute the article, and certify that they have the right to grant this license, certify that the work is available under either the Creative Commons Attribution license, or the Creative Commons Attribution-Noncommercial-ShareAlike license, and that they have the right to grant this license, or certify that the work is in the public domain (http://arxiv.org/help/license)
dc.subjectMarkov chains
dc.subjectStationary distribution
dc.subjectFirst passage times
dc.subjectHitting times
dc.subjectMixing times
dc.subjecttime to stationarity
dc.subjectKemeny constant
dc.subjectdistributions
dc.titleThe distribution of Mixing Times in Markov Chains
dc.typeCommissioned Report
dc.rights.accessrightsOpenAccess


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