The distribution of Mixing Times in Markov Chains
aut.embargo | false | |
aut.researcher | Hunter, Jeffrey Joseph | |
dc.contributor.author | Hunter, JJ | |
dc.date.accessioned | 2012-01-19T22:07:38Z | |
dc.date.available | 2012-01-19T22:07:38Z | |
dc.date.copyright | 2011-11-01 | |
dc.date.issued | 2011-11-01 | |
dc.description.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 [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.identifier.citation | arXiv:1111.0151 | |
dc.identifier.uri | https://hdl.handle.net/10292/3280 | |
dc.publisher | arXiv | |
dc.relation.uri | http://arxiv.org/abs/1111.0151 | |
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dc.rights.accessrights | OpenAccess | |
dc.subject | Markov chains | |
dc.subject | Stationary distribution | |
dc.subject | First passage times | |
dc.subject | Hitting times | |
dc.subject | Mixing times | |
dc.subject | time to stationarity | |
dc.subject | Kemeny constant | |
dc.subject | distributions | |
dc.title | The distribution of Mixing Times in Markov Chains | |
dc.type | Commissioned Report | |
pubs.organisational-data | /AUT | |
pubs.organisational-data | /AUT/Design & Creative Technologies | |
pubs.organisational-data | /AUT/Design & Creative Technologies/School of Computing & Mathematical Science | |
pubs.organisational-data | /AUT/PBRF Researchers | |
pubs.organisational-data | /AUT/PBRF Researchers/Design & Creative Technologies PBRF Researchers | |
pubs.organisational-data | /AUT/PBRF Researchers/Design & Creative Technologies PBRF Researchers/DCT C & M Management & Allied |