COLLINS, Benoit; LAMARRE, Pierre Yves Gaudreau; MALE, Camille

Metadatos

Mostrar el registro completo del ítem

Licencia de uso del documento

COLLINS, Benoit
Kyoto University

LAMARRE, Pierre Yves Gaudreau
Princeton University

MALE, Camille
Institut de Mathématiques de Bordeaux [IMB]

Idioma

Document de travail - Pré-publication

Resumen en inglés

In this paper, we pursue our study of asymptotic properties of families of random matrices that have a tensor structure. In previous work, the first- and second-named authors provided conditions under which tensor products of unitary random matrices are asymptotically free with respect to the normalized trace. Here, we extend this result by proving that asymptotic freeness of tensor products of Haar unitary matrices holds with respect to a significantly larger class of states. Our result relies on invariance under the symmetric group, and therefore on traffic probability. As a byproduct, we explore two additional generalisations: (i) we state results of freeness in a context of general sequences of representations of the unitary group -- the fundamental representation being a particular case that corresponds to the classical asymptotic freeness result for Haar unitary matrices, and (ii) we consider actions of the symmetric group and the free group simultaneously and obtain a result of asymptotic freeness in this context as well.< Leer menos

Metadatos

Compartir este ítem

Licencia de uso del documento

Asymptotic Freeness of Unitary Matrices in Tensor Product Spaces for Invariant States

Idioma

Resumen en inglés

URI

Orígen

Centros de investigación