GUE Correlators and Large Genus Asymptotics

2025/10/30 by Zhao, Jiayi
#Combinatorics (math.CO) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph)

paper · doi:10.48550/arxiv.2510.26137

Abstract

In this paper, we use a formula obtained in [8] to study certain asymptotic behaviors of GUE (Gaussian unitary ensemble) correlators. More precisely, we obtain large genus asymptotics of enumerations of ordinary graphs and ribbon graphs with 1 face.

Citations

• Combinatorics and large genus asymptotics of the Brézin--Gross--Witten numbers
• The factorial growth of topological recursion
• Resurgent large genus asymptotics of intersection numbers
• The matrix-resolvent method to tau-functions for the nonlinear Schrödinger hierarchy
• On the large genus asymptotics of psi-class intersection numbers
• Masur-Veech volumes, frequencies of simple closed geodesics and intersection numbers of moduli spaces of curves
• Hermitian One-Matrix Model and KP Hierarchy
• Determinantal formulae and loop equations

Related

• High order expansion of matrix models and enumeration of maps
• An asymptotic link between LUE and GUE and its spectral interpretation
• A homological approach to the Gaussian Unitary Ensemble
• The Singular Values of the GUE (Less is More)
• Combinatorial aspects of Parraud's asymptotic expansion for GUE matrices