Orbit measures and interlaced determinantal point processes

TL;DR

This paper investigates the eigenvalue distributions of Hermitian matrix minors, showing they form determinantal point processes and providing explicit correlation kernels for these configurations.

Contribution

It establishes that eigenvalues of minors in Hermitian matrices form determinantal processes and derives their correlation kernels, advancing understanding of their probabilistic structure.

Findings

Eigenvalues of matrix minors form determinantal point processes

Explicit correlation kernels are derived for these processes

The results apply to Hermitian matrices from classical complex Lie algebras

Abstract

We study some random interlaced configurations considering the eigenvalues of the main minors of Hermitian random matrices of the classical complex Lie algebras. We claim that these random configurations are determinantal and give their correlation kernels.