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

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.

arXiv comment35 pages, 35 figures, research borne out of collaboration at the MATRIX program 'Log-gases in Caeli Australi'