High order expansion of matrix models and enumeration of maps

2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/115327Perturbation of the GUE are known in physics to be related to enumeration of graphs on surfaces. We investigate this idea and show that for a small convex perturbation, we can perform a genus expansion: the moments of the empirical measure can be developed into a series whose g-th term is a generating function of graphs on a surface of genus g.35 pages, 3 figuresProbabilityCombinatorics15A52; 05C30High order expansion of matrix models and enumeration of mapstext