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

2025/10/25 by Rahman, Anas A., George, Daniel Munoz, Mingo, James A.
#05A19 #15B52 (Primary) 05C10 #46L54 (Secondary) #Combinatorics (math.CO) #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.2510.22308

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/N² correction terms of said moments and their equivalents for the GUE and LUE.

Citations

• Asymptotic limit of cumulants and higher order free cumulants of complex Wigner matrices
• Recursive characterisations of random matrix ensembles and associated combinatorial objects
• The Asymptotic Infinitesimal Distribution of a Real Wishart Random Matrix
• Joint Global Fluctuations of complex Wigner and deterministic Matrices
• Counting genus one partitions and permutations
• Evaluation of ensemble averages for simple Hamiltonians perturbed by a GOE interaction
• A planar diagram theory for strong interactions
• On the Distribution of the Roots of Certain Symmetric Matrices

Related

• Power counting in the spectral action matrix model
• Recursive characterisations of random matrix ensembles and associated combinatorial objects
• GUE Correlators and Large Genus Asymptotics
• Distributions of consecutive level spacings of circular unitary ensemble and their ratio: finite-size corrections and Riemann ζ zeros
• Pairwise Difference Representations of Moments: Gini and Generalized Lagrange identities