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)

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
• 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

Project Code	Award No	Project Name	Principal Investigator	Funder's Name	Funder Ref	Lead Dept
305944		Multilayer Algorithmics to Leverage Graph Structure	Kitty Meeks	Engineering and Physical Sciences Research Council (EPSRC)	EP/T004878/1	M&S - Statistics