2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/56937We consider a set of probability measures on a finite event space $Ω$. The mutual affinity is introduced in terms of the spectrum of the associated Gram matrix. We show that, for randomly chosen measures, the empirical eigenvalue distribution of the Gram matrix converges to a fixed distribution in the limit where the number of measures, together with the cardinality of $Ω$, goes to infinity.24 pagesMathematical PhysicsProbability28A33, 60G57, 60F10text