2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/70274Some general connections between martingales and character ratios of finite groups are developed. As an application we sharpen the convergence rate in a central limit theorem for the character ratio of a random representation of the symmetric group on transpositions. A generalization of these results is given for Jack measure on partitions. We also give a probabilistic proof of a result of Burnside and Brauer on the decomposition of tensor products.22 pagesRepresentation TheoryProbabilitytext