A noncommutative extended de Finetti theorem

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dc.creatorKöstler, Claus
dc.date2008-06-23
dc.date.accessioned2026-07-07T09:46:07Z
dc.date.available2026-07-07T09:46:07Z
dc.descriptionThe extended de Finetti theorem characterizes exchangeable infinite random sequences as conditionally i.i.d. and shows that the apparently weaker distributional symmetry of spreadability is equivalent to exchangeability. Our main result is a noncommutative version of this theorem. In contrast to the classical result of Ryll-Nadzewski, exchangeability turns out to be stronger than spreadability for infinite noncommutative random sequences. Out of our investigations emerges noncommutative conditional independence in terms of a von Neumann algebraic structure closely related to Popa's notion of commuting squares and Kümmerer's generalized Bernoulli shifts. Our main result is applicable to classical probability, quantum probability, in particular free probability, braid group representations and Jones subfactors.
dc.description44 pages
dc.identifierhttps://arxiv.org/abs/0806.3621
dc.identifierhttp://arxiv.org/abs/0806.3621
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/163423
dc.subjectOperator Algebras
dc.subjectProbability
dc.subject46L53; 60G09; 47A53
dc.titleA noncommutative extended de Finetti theorem
dc.typetext

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