2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/123956We give a streamlined proof of a quantitative version of a result from [DG1] which is crucial for the proof of universality in the bulk [DG1] and also at the edge [DG2] for orthogonal and symplectic ensembles of random matrices. As a byproduct, this result gives asymptotic information on a certain ratio of the beta=1,2,4 partition functions for log gases.9 pagesMathematical PhysicsClassical Analysis and ODEs15A52text