2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/146189It is shown that the combinatorics of commutation relations is well suited for analyzing the convergence rate of certain Markov chains. Examples studied include random walk on irreducible representations, a local random walk on partitions whose stationary distribution is the Ewens distribution, and some birth-death chains.37 pages; referee suggestions implemented, discuss up-down chains as well, slightly better bounds in Props. 5.6, 7.6ProbabilityCombinatoricstext