Rectangular random matrices, related free entropy and free Fisher's information
| dc.creator | Benaych-Georges, Florent | |
| dc.date | 2005-12-04 | |
| dc.date.accessioned | 2026-07-07T06:54:50Z | |
| dc.date.available | 2026-07-07T06:54:50Z | |
| dc.description | We prove that independent rectangular random matrices, when embedded in a space of larger square matrices, are asymptotically free with amalgamation over a commutative finite dimensional subalgebra $D$ (under an hypothesis of unitary invariance). Then we consider elements of a finite von Neumann algebra containing $D$, which have kernel and range projection in $D$. We associate them a free entropy with the microstates approach, and a free Fisher's information with the conjugate variables approach. Both give rise to optimization problems whose solutions involve freeness with amalgamation over $D$. It could be a first proposition for the study of operators between different Hilbert spaces with the tools of free probability. As an application, we prove a result of freeness with amalgamation between the two parts of the polar decomposition of $R$-diagonal elements with non trivial kernel. | |
| dc.description | 41 pages | |
| dc.identifier | https://arxiv.org/abs/math/0512081 | |
| dc.identifier | http://arxiv.org/abs/math/0512081 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/106079 | |
| dc.subject | Operator Algebras | |
| dc.subject | Probability | |
| dc.subject | 46L54;15A52 | |
| dc.title | Rectangular random matrices, related free entropy and free Fisher's information | |
| dc.type | text |