2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/58925First we survey generating function methods for obtaining useful probability estimates about random matrices in the finite classical groups. Then we describe a probabilistic picture of conjugacy classes which is coherent and beautiful. Connections are made with symmetric function theory, Markov chains, potential theory, Rogers-Ramanujan type identities, quivers, and various measures on partitions.This is much improved--less biased toward my own work and more substanceGroup TheoryCombinatoricsProbabilitytext