Commutation relations and Markov chains

Abstract

It 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, 7.6