Some minimization problems for the free analogue of the Fisher information
| dc.creator | Nica, A. | |
| dc.creator | Shlyakhtenko, D. | |
| dc.creator | Speicher, R. | |
| dc.date | 1998-09-16 | |
| dc.date.accessioned | 2026-07-07T05:26:01Z | |
| dc.date.available | 2026-07-07T05:26:01Z | |
| dc.description | We consider the free non-commutative analogue Phi^*, introduced by D. Voiculescu, of the concept of Fisher information for random variables. We determine the minimal possible value of Phi^*(a,a^*), if a is a non-commutative random variable subject to the constraint that the distribution of aa^* is prescribed. More generally, we obtain the minimal possible value of Phi^*({a_{ij},a_{ij}^*), if {a_{ij}} is a family of non-commutative random variables such that the distribution of AA^* is prescribed, where A is the matrix (a_{ij}). The d*d-generalization is obtained from the case d=1 via a result of independent interest, concerning the minimal value of Phi^*({a_{ij},a_{ij}^*), when the matrix A=(a_{ij}) and its adjoint have a given joint distribution. We then show how the minimization results obtained for Phi^* lead to maximization results concerning the free entropy chi^*, also defined by Voiculescu. | |
| dc.description | 31 pages, Latex | |
| dc.identifier | https://arxiv.org/abs/math/9809080 | |
| dc.identifier | http://arxiv.org/abs/math/9809080 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/77400 | |
| dc.subject | Operator Algebras | |
| dc.subject | Probability | |
| dc.title | Some minimization problems for the free analogue of the Fisher information | |
| dc.type | text |