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Rapport (Rapport De Recherche) Année : 2022

On cover times of Markov chains

Résumé

We consider the cover time of a discrete-time homogenous Markov chain, that is the time needed by the Markov chain to visit all its states. We analyze both the distribution and the moments of the cover time and we are interested in exact results instead of asymptotic values of the mean cover time which are generally considered in the literature. We first obtain several general results on the hitting time and the cover time of a subset of the state space both in terms of distribution and moments. These results are then applied to particular graphs namely the generalized cycle graph, the complete graph and the generalized path graph. They lead to recurrence or analytic relations for the distribution and the mean value of their cover times.
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Dates et versions

hal-03837323 , version 1 (02-11-2022)

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Paternité

Identifiants

  • HAL Id : hal-03837323 , version 1

Citer

Bruno Sericola. On cover times of Markov chains. Inria Rennes - Bretagne Atlantique. 2022, pp.32. ⟨hal-03837323⟩
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