Corrections to Classical Matrix Ensemble Moments, Non-Crossing Annular Pairings, and Ribbon Graphs

TL;DR

This paper explores the combinatorial structures underlying the $1/N$ corrections in spectral moments of classical random matrix ensembles, establishing bijections with ribbon graphs and non-crossing pairings.

Contribution

It introduces new combinatorial objects for higher-order corrections and connects them to ribbon graphs and non-crossing pairings for classical ensembles.

Findings

Bijection between ribbon graphs and non-crossing annular pairings for GOE and LOE.

Derived combinatorial objects for $1/N^2$ correction terms for GUE and LUE.

Enhanced understanding of spectral moment corrections in random matrix theory.

Abstract

We elucidate a bijection between ribbon graphs on the real projective plane and non-crossing annular pairings that relate to the $1/N$ correction term of the GOE and LOE spectral moments. We also derive analogous objects for the $1/N^2$ correction terms of said moments and their equivalents for the GUE and LUE.