Non-crossing cumulants of type B
| dc.creator | Biane, Philippe | |
| dc.creator | Goodman, Frederick | |
| dc.creator | Nica, Alexandru | |
| dc.date | 2002-06-17 | |
| dc.date.accessioned | 2026-07-07T04:49:10Z | |
| dc.date.available | 2026-07-07T04:49:10Z | |
| dc.description | We establish connections between the lattices of non-crossing partitions of type B introduced by V. Reiner, and the framework of the free probability theory of D. Voiculescu. Lattices of non-crossing partitions (of type A, up to now) have played an important role in the combinatorics of free probability, primarily via the non-crossing cumulants of R. Speicher. Here we introduce the concept of {\em non-crossing cumulant of type B;} the inspiration for its definition is found by looking at an operation of ``restricted convolution of multiplicative functions'', studied in parallel for functions on symmetric groups (in type A) and on hyperoctahedral groups (in type B). The non-crossing cumulants of type B live in an appropriate framework of ``non-commutative probability space of type B'', and are closely related to a type B analogue for the R-transform of Voiculescu (which is the free probabilistic counterpart of the Fourier transform). By starting from a condition of ``vanishing of mixed cumulants of type B'', we obtain an analogue of type B for the concept of free independence for random variables in a non-commutative probability space. | |
| dc.description | 48 pages, latex | |
| dc.identifier | https://arxiv.org/abs/math/0206167 | |
| dc.identifier | http://arxiv.org/abs/math/0206167 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/64321 | |
| dc.subject | Operator Algebras | |
| dc.subject | Combinatorics | |
| dc.subject | 46L54; 05A18 | |
| dc.title | Non-crossing cumulants of type B | |
| dc.type | text |