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On cover times of Markov chains

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Bibliographic Details
Title: On cover times of Markov chains
Authors: Sericola, Bruno
Contributors: mEasuRing and ManagIng Network operation and Economic (ERMINE), Inria Rennes – Bretagne Atlantique, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-RÉSEAUX, TÉLÉCOMMUNICATION ET SERVICES (IRISA-D2), Institut de Recherche en Informatique et Systèmes Aléatoires (IRISA), Université de Rennes (UR)-Institut National des Sciences Appliquées - Rennes (INSA Rennes), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université de Bretagne Sud (UBS)-École normale supérieure - Rennes (ENS Rennes)-Institut National de Recherche en Informatique et en Automatique (Inria)-CentraleSupélec-Centre National de la Recherche Scientifique (CNRS)-IMT Atlantique (IMT Atlantique), Institut Mines-Télécom Paris (IMT)-Institut Mines-Télécom Paris (IMT)-Université de Rennes (UR)-Institut National des Sciences Appliquées - Rennes (INSA Rennes), Institut Mines-Télécom Paris (IMT)-Institut Mines-Télécom Paris (IMT)-Institut de Recherche en Informatique et Systèmes Aléatoires (IRISA), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université de Bretagne Sud (UBS)-École normale supérieure - Rennes (ENS Rennes)-CentraleSupélec-Centre National de la Recherche Scientifique (CNRS)-IMT Atlantique (IMT Atlantique), Institut Mines-Télécom Paris (IMT)-Institut Mines-Télécom Paris (IMT)
Source: ISSN: 1532-6349.
Publisher Information: HAL CCSD
INFORMS (Institute for Operations Research and Management Sciences)
Publication Year: 2023
Collection: Archive ouverte HAL (Hyper Article en Ligne, CCSD - Centre pour la Communication Scientifique Directe)
Subject Terms: Markov chain, Hitting time, Cover time, Cycle graph, Complete graph, Path graph, [MATH]Mathematics [math], [INFO]Computer Science [cs]
Description: International audience ; We consider the cover time of a discrete-time homogenous Markov chain, that isthe 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.
Document Type: article in journal/newspaper
Language: English
Relation: hal-04364216; https://inria.hal.science/hal-04364216; https://inria.hal.science/hal-04364216/document; https://inria.hal.science/hal-04364216/file/LastCover.pdf
Availability: https://inria.hal.science/hal-04364216
https://inria.hal.science/hal-04364216/document
https://inria.hal.science/hal-04364216/file/LastCover.pdf
Rights: http://creativecommons.org/licenses/by-nc/ ; info:eu-repo/semantics/OpenAccess
Accession Number: edsbas.C0FF6AA5
Database: BASE
Description
Abstract:International audience ; We consider the cover time of a discrete-time homogenous Markov chain, that isthe 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.