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Multiple equilibria of nonhomogeneous Markov chains and self-validating web rankings

dc.rights.licenseOTHen_US
dc.contributor.authorAkian, Marianne
dc.contributor.authorGaubert, Stéphane
dc.contributor.authorNINOVE, Laure
dc.date.accessioned2021-09-14T15:03:51Z
dc.date.available2021-09-14T15:03:51Z
dc.date.issued2008-01
dc.identifier.urihttps://luck.synhera.be/handle/123456789/1144
dc.identifier.doihttps://www.researchgate.net/publication/1901648_Multiple_equilibria_of_nonhomogeneous_Markov_chains_and_self-validating_web_rankingsen_US
dc.description.abstractPageRank is a ranking of the web pages that measures how often a given web page is visited by a random surfer on the web graph, for a simple model of web surfing. It seems realistic that PageRank may also have an influence on the behavior of web surfers. We propose here a simple model taking into account the mutual influence between web ranking and web surfing. Our ranking, the T-PageRank, is a nonlinear generalization of the PageRank. It is defined as the limit, if it exists, of some nonlinear iterates. A positive parameter T, the temperature, measures the confidence of the web surfer in the web ranking. We prove that, when the temperature is large enough, the T-PageRank is unique and the iterates converge globally on the domain. But when the temperature is small, there may be several T-PageRanks, that may strongly depend on the initial ranking. Our analysis uses results of nonlinear Perron-Frobenius theory, Hilbert projective metric and Birkhoff's coefficient of ergodicity.en_US
dc.description.sponsorshipOTHen_US
dc.language.isoENen_US
dc.publisher/en_US
dc.relation.isreferencedbyValverde-Albacete, Francisco J. & Peláez-Moreno, Carmen. (2017). A Formal Concept Analysis Look at the Analysis of Affiliation Networks. 10.1007/978-3-319-64167-6_7en_US
dc.relation.isreferencedbyWicker, Andrew & Doyle, Jon. (2012). Leveraging Multiple Mechanisms for Information Propagation. 10.1007/978-3-642-27216-5_1en_US
dc.rights.urihttps://arxiv.org/help/licenseen_US
dc.subjectMathématiquesen_US
dc.subjectProbabilitésen_US
dc.subjectThéorie des systèmes dynamiquesen_US
dc.subject.enProbabilityen_US
dc.subject.enDynamical Systemsen_US
dc.subject.enMarkov chainsen_US
dc.subject.enPageRanken_US
dc.titleMultiple equilibria of nonhomogeneous Markov chains and self-validating web rankingsen_US
dc.typeArticle scientifiqueen_US
synhera.classificationPhysique, chimie, mathématiques & sciences de la terre>>Mathématiquesen_US
synhera.classificationIngénierie, informatique & technologie>>Sciences informatiquesen_US
synhera.institutionHE Léonard de Vincien_US
synhera.otherinstitutionNational Institute for Research in Computer Science and Controlen_US
dc.description.versionOuien_US
dc.rights.holder/en_US


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