Orbit measures, random matrix theory and interlaced determinantal processes

Details Orbit measures, random matrix theory and interlaced determinantal processes Orbit measures, random matrix theory and interlaced determinantal processes

2008-10-06

arxiv.org/abs/0810.1011v2

Mathematics

Probability

Scientific paper

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 mulltiplicities. We show that a large class of them are determinantal.

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