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

John Sylvester

Statistics & Probability Letters, 2022, vol. 187, issue C

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.

Keywords: Cover time; Markov chain; Rational number; Multiple random walk (search for similar items in EconPapers)
Date: 2022
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Citations: View citations in EconPapers (1)

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DOI: 10.1016/j.spl.2022.109534

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