Sylvester, J. (2022) The cover time of a (multiple) Markov chain with rational transition probabilities is rational. Statistics and Probability Letters, 187, 109534. (doi: 10.1016/j.spl.2022.109534)
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Abstract
The cover time of a Markov chain on a finite state space is the expected time until all states are visited. We show that if the cover time of a discrete-time Markov chain with rational transitions probabilities is bounded, then it is a rational number. The result is proved by relating the cover time of the original chain to the hitting time of a set in another higher dimensional chain. We prove this result in a more general setting where k ≥ 1 independent copies of a Markov chain are run simultaneously on the same state space.
Item Type: | Articles |
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Additional Information: | The author is currently supported by Engineering and Physical Sciences Research Council (ESPRC) grant number EP/T004878/1. This work was started while the author was supported by ERC Starting Grant no. 679660 at the University of Cambridge. |
Status: | Published |
Refereed: | Yes |
Glasgow Author(s) Enlighten ID: | Sylvester, Dr John |
Authors: | Sylvester, J. |
College/School: | College of Science and Engineering > School of Computing Science |
Journal Name: | Statistics and Probability Letters |
Publisher: | Elsevier |
ISSN: | 0167-7152 |
ISSN (Online): | 1879-2103 |
Published Online: | 07 May 2022 |
Copyright Holders: | Crown Copyright © 2022 |
First Published: | First published in Statistics and Probability Letters 187:109534 |
Publisher Policy: | Reproduced under a Creative Commons Licence |
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