Breakdown of Universality in Random Matrix Models

TL;DR

This paper investigates how adding trace product terms to the potential in a large random matrix model affects the universality of eigenvalue correlations, showing that universality is broken under these modifications.

Contribution

It introduces a calculation of smoothed correlators in a random matrix model with trace product terms, revealing deviations from universal behavior.

Findings

Connected eigenvalue correlations receive non-universal corrections.

Universality in eigenvalue correlations is broken by trace product terms.

The model extends previous universality results to more complex potentials.

Abstract

We calculate smoothed correlators for a large random matrix model with a potential containing products of two traces $\tr W_1(M) \cdot \tr W_2(M)$ in addition to a single trace $\tr V(M)$. Connected correlation function of density eigenvalues receives corrections besides the universal part derived by Brezin and Zee and it is no longer universal in a strong sense.