Multilinear function series and transforms in free probability theory
| dc.creator | Dykema, Ken | |
| dc.date | 2005-04-18 | |
| dc.date | 2005-06-05 | |
| dc.date.accessioned | 2026-07-07T05:19:12Z | |
| dc.date.available | 2026-07-07T05:19:12Z | |
| dc.description | The 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.description | 54 pages. (In the revised version, only minor changes were made.) | |
| dc.identifier | https://arxiv.org/abs/math/0504361 | |
| dc.identifier | http://arxiv.org/abs/math/0504361 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/74937 | |
| dc.subject | Operator Algebras | |
| dc.subject | Combinatorics | |
| dc.subject | Rings and Algebras | |
| dc.subject | 46L54; 16W60, 05A05 | |
| dc.title | Multilinear function series and transforms in free probability theory | |
| dc.type | text |