Universal Wide Correlators in Non-Gaussian Orthogonal, Unitary and Symplectic Random Matrix Ensembles

TL;DR

This paper develops a method to compute universal wide distance correlators in non-Gaussian random matrix ensembles across orthogonal, unitary, and symplectic classes, using loop equations in the 1/N-expansion.

Contribution

It introduces an algorithm to calculate connected correlators to any order in the 1/N-expansion for these ensembles, demonstrating universality in the large N limit.

Findings

Multi-level correlator is universal at large N.

Algorithm for arbitrary order in 1/N-expansion.

Connected correlators computed via loop equations.

Abstract

We calculate wide distance connected correlators in non-gaussian orthogonal, unitary and symplectic random matrix ensembles by solving the loop equation in the 1/N-expansion. The multi-level correlator is shown to be universal in large N limit. We show the algorithm to obtain the connected correlator to an arbitrary order in the 1/N-expansion.