Multilinear function series and transforms in free probability theory

dc.creatorDykema, Ken
dc.date2005-04-18
dc.date2005-06-05
dc.date.accessioned2026-07-07T05:19:12Z
dc.date.available2026-07-07T05:19:12Z
dc.descriptionThe algebra Mul[[B]] of formal multilinear function series over an algebra B and its quotient SymMul[[B]] are introduced, as well as corresponding operations of formal composition. In the setting of Mul[[B]], the unsymmetrized R- and T-transforms of random variables in B-valued noncommutative probability spaces are introduced. These satisfy properties analogous to the usual R- and T-transforms, (the latter being just the reciprocal of the S-transform), but describe all moments of a random variable, not only the symmetric moments. The partially ordered set of noncrossing linked partitions is introduced and is used to prove properties of the unsymmetrized T-transform.
dc.description54 pages. (In the revised version, only minor changes were made.)
dc.identifierhttps://arxiv.org/abs/math/0504361
dc.identifierhttp://arxiv.org/abs/math/0504361
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/74937
dc.subjectOperator Algebras
dc.subjectCombinatorics
dc.subjectRings and Algebras
dc.subject46L54; 16W60, 05A05
dc.titleMultilinear function series and transforms in free probability theory
dc.typetext

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