IDEAS home Printed from https://ideas.repec.org/a/wsi/apjorx/v30y2013i01ns0217595912500455.html
   My bibliography  Save this article

The Distribution Of Mixing Times In Markov Chains

Author

Listed:
  • JEFFREY J. HUNTER

    (School of Computing & Mathematical Sciences, Auckland University of Technology, Auckland, New Zealand)

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, JJ (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, JJ (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.

Suggested Citation

  • Jeffrey J. Hunter, 2013. "The Distribution Of Mixing Times In Markov Chains," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 30(01), pages 1-29.
    • Handle: RePEc:wsi:apjorx:v:30:y:2013:i:01:n:s0217595912500455
    DOI: 10.1142/S0217595912500455
    as

    Download full text from publisher

    File URL: http://www.worldscientific.com/doi/abs/10.1142/S0217595912500455
    Download Restriction: Access to full text is restricted to subscribers
    File URL: https://libkey.io/10.1142/S0217595912500455?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:wsi:apjorx:v:30:y:2013:i:01:n:s0217595912500455. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no bibliographic references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Tai Tone Lim (email available below). General contact details of provider: http://www.worldscinet.com/apjor/apjor.shtml .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.