Information Geometry of Random Matrix Models
| dc.creator | Shiber, Dan | |
| dc.date | 2006-09-13 | |
| dc.date | 2007-04-19 | |
| dc.date.accessioned | 2026-07-07T07:57:14Z | |
| dc.date.available | 2026-07-07T07:57:14Z | |
| dc.description | In this paper we develop the theory of information geometry for single random matrix models, with two goals: proving a Cramer-Rao theorem for estimators on random matrices, and calculating the Legendre transform of pressure and entropy with respect to a metric duality. Consequently, in the large n limit we recover several quantities from free probability: Voiculescu's conjugate variable is the tangent vector to the GUE perturbation model, giving rise to a metric which turns out to be the free Fisher information measure; Hiai's Legendre transform of free pressure agrees with our Legendre transform of pressure; and Speicher's covariance of fluctuations naturally arises as the metric on the random matrix model obtained from the fluctuation functions. | |
| dc.description | 29 pages, no figures; corrected typos, a few sections revised | |
| dc.identifier | https://arxiv.org/abs/math/0609372 | |
| dc.identifier | http://arxiv.org/abs/math/0609372 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/127571 | |
| dc.subject | Operator Algebras | |
| dc.subject | Probability | |
| dc.subject | 15A52 Random matrices | |
| dc.title | Information Geometry of Random Matrix Models | |
| dc.type | text |