Operations on certain non-commutative operator-valued random variables. (English) Zbl 0839.46060
Connes, A. (ed.), Recent advances in operator algebras. Collection of talks given in the conference on operator algebras held in Orléans, France in July 1992. Paris: Société Mathématique de France, Astérisque. 232, 243-275 (1995).
Summary: In the context of free products with amalgamation over an algebra \(B\), additive and multiplicative free convolutions are studied. Analogues of the \(R\)- and \(S\)-transforms are obtained. Applications to the \(B\)-free central limit theorem and to the spectra of convolution operators on free groups are considered.
For the entire collection see [Zbl 0832.00041].
For the entire collection see [Zbl 0832.00041].
MSC:
| 46L51 | Noncommutative measure and integration |
| 46L53 | Noncommutative probability and statistics |
| 46L54 | Free probability and free operator algebras |
| 60F99 | Limit theorems in probability theory |
| 43A99 | Abstract harmonic analysis |
