Matrices coupled in a chain. I. Eigenvalue correlations

TL;DR

This paper derives a determinant-based correlation function for eigenvalues of multiple coupled complex Hermitian matrices arranged in a chain, extending Dyson's theorem.

Contribution

It generalizes Dyson's theorem to compute eigenvalue correlations for a chain of coupled matrices, providing a new analytical tool.

Findings

Eigenvalue correlations expressed as a single determinant

Extension of Dyson's theorem to coupled matrices

Analytical framework for complex Hermitian matrix chains

Abstract

The general correlation function for the eigenvalues of $p$ complex hermitian matrices coupled in a chain is given as a single determinant. For this we use a slight generalization of a theorem of Dyson.