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dc.contributor.authorEbrahimi-Fard, Kurusch
dc.contributor.authorPatras, Frederic
dc.date.accessioned2019-07-09T05:38:12Z
dc.date.available2019-07-09T05:38:12Z
dc.date.created2018-01-17T23:50:24Z
dc.date.issued2018
dc.identifier.citationAdvances in Mathematics. 2018, 328 112-132.nb_NO
dc.identifier.issn0001-8708
dc.identifier.urihttp://hdl.handle.net/11250/2603776
dc.description.abstractThe theory of cumulants is revisited in the “Rota way”, that is, by following a combinatorial Hopf algebra approach. Monotone, free, and boolean cumulants are considered as infinitesimal characters over a particular combinatorial Hopf algebra. The latter is neither commutative nor cocommutative, and has an underlying unshuffle bialgebra structure which gives rise to a shuffle product on its graded dual. The moment-cumulant relations are encoded in terms of shuffle and half-shuffle exponentials. It is then shown how to express concisely monotone, free, and boolean cumulants in terms of each other using the pre-Lie Magnus expansion together with shuffle and half-shuffle logarithms.nb_NO
dc.language.isoengnb_NO
dc.publisherElseviernb_NO
dc.relation.urihttp://linkinghub.elsevier.com/retrieve/pii/S0001870818300112
dc.titleMonotone, free, and boolean cumulants: a shuffle algebra approachnb_NO
dc.typeJournal articlenb_NO
dc.typePeer reviewednb_NO
dc.description.versionpublishedVersionnb_NO
dc.source.pagenumber112-132nb_NO
dc.source.volume328nb_NO
dc.source.journalAdvances in Mathematicsnb_NO
dc.identifier.doi10.1016/j.aim.2018.01.003
dc.identifier.cristin1545888
dc.description.localcodeThis article will not be available due to copyright restrictions (c) 2018 by Elseviernb_NO
cristin.unitcode194,63,15,0
cristin.unitnameInstitutt for matematiske fag
cristin.ispublishedtrue
cristin.fulltextoriginal
cristin.qualitycode2


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