Diagrammatic Method for Wide Correlators in Gaussian Orthogonal and Symplectic Random Matrix Ensembles

TL;DR

This paper introduces a diagrammatic approach to compute connected correlators in time-dependent Gaussian orthogonal and symplectic random matrix ensembles, providing explicit calculations of Green's functions and multi-level correlators.

Contribution

It presents a novel diagrammatic method for calculating correlators in these ensembles, including leading order Green's functions and higher-order multi-level correlators.

Findings

Derived leading order one-point Green's functions

Computed wide two-level correlators in the first nontrivial order

Calculated wide three-level correlators using planar diagrams

Abstract

We calculate connected correlators in time dependent Gaussian orthogonal and symplectic random matrix ensembles by a diagrammatic method. We obtain averaged one-point Green's functions in the leading order O(1) and wide two-level and three-level correlators in the first nontrivial order by summing over twisted and untwisted planer diagrams.