A connection between representation of compact groups and some invariant ensembles of Hermitian matrices is described. We focus on two types of invariant ensembles which extend the Gaussian and the Laguerre Unitary ensembles. We study them using projections and convolutions of invariant probability measures on adjoint orbits of a compact Lie group. These measures are described by semiclassical approximation involving tensor and restriction multiplicities. We show that a large class of them are determinantal.
Publié le : 2010-02-15
Classification:
Random matrix,
Determinantal process,
Interlaced configuration,
Gelfand Tsetlin polytope,
Cristal graph,
Minor process,
Rank one perturbation,
15A52,
17B10
@article{1267454115,
author = {Defosseux, Manon},
title = {Orbit measures, random matrix theory and interlaced determinantal processes},
journal = {Ann. Inst. H. Poincar\'e Probab. Statist.},
volume = {46},
number = {1},
year = {2010},
pages = { 209-249},
language = {en},
url = {http://dml.mathdoc.fr/item/1267454115}
}
Defosseux, Manon. Orbit measures, random matrix theory and interlaced determinantal processes. Ann. Inst. H. Poincaré Probab. Statist., Tome 46 (2010) no. 1, pp. 209-249. http://gdmltest.u-ga.fr/item/1267454115/