Operator-valued distributions: I. Characterizations of freeness
| dc.creator | Nica, Alexandru | |
| dc.creator | Shlyakhtenko, Dimitri | |
| dc.creator | Speicher, Roland | |
| dc.date | 2001-12-31 | |
| dc.date.accessioned | 2026-07-07T04:45:37Z | |
| dc.date.available | 2026-07-07T04:45:37Z | |
| dc.description | Let $M$ be a $B$-probability space. Assume that $B$ itself is a $D$-probability space; then $M$ can be viewed as $D$-probability space as well. Let $X$ be in $M$. We look at the question of relating the properties of $X$ as $B$-valued random variable to its properties as $D$-valued random variable. We characterize freeness of $X$ from $B$ with amalgamation over $D$: (a) in terms of a certain factorization condition linking the $B$-valued and $D$-valued cumulants of $X$, and (b) for $D$ finite-dimensional, in terms of linking the $B$-valued and the $D$-valued Fisher information of $X$. We give an application to random matrices. For the second characterization we derive a new operator-valued description of the conjugate variable and introduce an operator-valued version of the liberation gradient. | |
| dc.identifier | https://arxiv.org/abs/math/0201001 | |
| dc.identifier | http://arxiv.org/abs/math/0201001 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/63018 | |
| dc.subject | Operator Algebras | |
| dc.subject | Probability | |
| dc.subject | 46L54 | |
| dc.title | Operator-valued distributions: I. Characterizations of freeness | |
| dc.type | text |