The cover time of a (multiple) Markov chain with rational transition probabilities is rational

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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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
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.
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
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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Project CodeAward NoProject NamePrincipal InvestigatorFunder's NameFunder RefLead Dept
305944Multilayer Algorithmics to Leverage Graph StructureKitty MeeksEngineering and Physical Sciences Research Council (EPSRC)EP/T004878/1M&S - Statistics