Orbit measures, random matrix theory and interlaced determinantal processes

Manon Defosseux

Annales de l'I.H.P. Probabilités et statistiques (2010)

  • Volume: 46, Issue: 1, page 209-249
  • ISSN: 0246-0203

Abstract

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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.

How to cite

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Defosseux, Manon. "Orbit measures, random matrix theory and interlaced determinantal processes." Annales de l'I.H.P. Probabilités et statistiques 46.1 (2010): 209-249. <http://eudml.org/doc/239800>.

@article{Defosseux2010,
abstract = {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.},
author = {Defosseux, Manon},
journal = {Annales de l'I.H.P. Probabilités et statistiques},
keywords = {random matrix; determinantal process; interlaced configuration; Gelfand Tsetlin polytope; cristal graph; minor process; rank one perturbation; crystal graph; eigenvalue distribution; random matrix ensembles; Gaussian and Laguerre unitary ensembles; orbit measure},
language = {eng},
number = {1},
pages = {209-249},
publisher = {Gauthier-Villars},
title = {Orbit measures, random matrix theory and interlaced determinantal processes},
url = {http://eudml.org/doc/239800},
volume = {46},
year = {2010},
}

TY - JOUR
AU - Defosseux, Manon
TI - Orbit measures, random matrix theory and interlaced determinantal processes
JO - Annales de l'I.H.P. Probabilités et statistiques
PY - 2010
PB - Gauthier-Villars
VL - 46
IS - 1
SP - 209
EP - 249
AB - 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.
LA - eng
KW - random matrix; determinantal process; interlaced configuration; Gelfand Tsetlin polytope; cristal graph; minor process; rank one perturbation; crystal graph; eigenvalue distribution; random matrix ensembles; Gaussian and Laguerre unitary ensembles; orbit measure
UR - http://eudml.org/doc/239800
ER -

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