Universal Behavior of Correlations between Eigenvalues of Random Matrices

TL;DR

This paper investigates the universal properties of connected correlations between eigenvalues of unitary random matrices through numerical simulations, revealing universal behavior after smoothing despite non-universal density and bare correlations.

Contribution

It demonstrates that connected correlations exhibit universal behavior post-smoothing, supported by Monte Carlo ensemble averaging.

Findings

Connected correlations become universal after smoothing.

Density and bare correlations are not universal.

Numerical evidence supports the universality of connected correlations.

Abstract

The universal connected correlations proposed recently between eigenvalues of unitary random matrices is examined numerically. We perform an ensemble average by the Monte Carlo sampling. Although density of eigenvalues and a bare correlation of the eigenvalues are not universal, the connected correlation shows a universal behavior after smoothing.