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 | |
| dc.rights | arXiv 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.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 |