2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/156423We point out that the transmission eigenvalue density and higher order correlation functions in chaotic cavities for an arbitrary number of incoming and outgoing leads $(N_1,N_2)$ are analytically known from the Jacobi ensemble of Random Matrix Theory. Using this result and a simple linear statistic, we give an exact and non-perturbative expression for moments of the form $<λ_1^m>$ for $m>-|N_1-N_2|-1$ and $β=2$, thus improving the existing results in the literature. Secondly, we offer an independent derivation of the average density and higher order correlation functions for $β=2,4$ which does not make use of the orthogonal polynomials technique. This result may be relevant for an efficient numerical implementation avoiding determinants.Slight extension of the published version. One reference added; main result (16) simplifiedMesoscale and Nanoscale PhysicsStatistical Mechanicstext