Replica Method for Wide Correlators in Gaussian Orthogonal, Unitary And Symplectic Random Matrix Ensembles

TL;DR

This paper employs the replica method to compute connected correlators in Gaussian random matrix ensembles, providing detailed results for Green's functions and multi-level correlators up to specific orders in 1/N expansion.

Contribution

It introduces a systematic replica method approach to calculate wide correlators in Gaussian ensembles, including higher-order corrections in 1/N expansion.

Findings

Calculated averaged one-point Green's functions up to O(1/N)

Derived wide two-level correlators up to O(1/N^2)

Obtained wide three-level correlators up to O(1/N^4)

Abstract

We calculate connected correlators in Gaussian orthogonal, unitary and symplectic random matrix ensembles by the replica method in the 1/N-expansion. We obtain averaged one-point Green's functions up to the next-to-leading order O(1/N) and wide two-level correlators up to the first nontrivial order O(1/N^2) and wide three-level correlators up to the first nontrivial order $O(1/N^4)$ by carefully treating fluctuations in saddle-point evaluation.