On the neighbor spacing of eigenvalues of unitary matrices

TL;DR

This paper discusses a subtle numerical error that can occur when calculating the eigenvalue spacing statistics of random unitary matrices, highlighting potential pitfalls in such computational analyses.

Contribution

It identifies and explains a specific subtle error in numerical methods used for eigenvalue spacing analysis of unitary matrices.

Findings

The error can significantly affect eigenvalue spacing statistics.

Awareness of this error improves the accuracy of numerical simulations.

Guidelines are provided to avoid this computational pitfall.

Abstract

We describe a subtle error which can appear in numerical calculations involving the spacing statistics of eigenvalues of random unitary matrices.