Convergence rates of Markov chains on spaces of partitions ∗

We study the convergence rate to stationarity for a class of exchangeable partitionvalued Markov chains called cut-and-paste chains. The law governing the transitions of a cut-and-paste chain is determined by products of i.i.d. stochastic matrices, which describe the chain induced on the simplex by taking asymptotic frequencies. Using this representation, we establish upper bounds for the mixing times of ergodic cutand-paste chains; and, under certain conditions on the distribution of the governing random matrices, we show that the “cutoff phenomenon” holds.