Matrices coupled in a chain. II. Spacing functions

TL;DR

This paper introduces a method to calculate spacing functions for eigenvalues of multiple coupled Hermitian matrices arranged in a chain, extending the classical single-matrix case.

Contribution

It generalizes the known single-matrix eigenvalue spacing results to a chain of coupled matrices, providing a new computational approach.

Findings

Derived a method for spacing functions of coupled matrices

Extended single-matrix eigenvalue spacing results to chains

Provides a framework for analyzing eigenvalue distributions in coupled systems

Abstract

For the eigenvalues of $p$ complex hermitian $n\times n$ matrices coupled in a chain, we give a method of calculating the spacing functions. This is a generalization of the one matrix case which has been known for a long time.