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Convergence rates of Markov chains on spaces of partitions. (English) Zbl 1296.60183

Summary: We study the convergence rate to stationarity for a class of exchangeable partition-valued Markov chains called cut-and-paste chains. The law governing the transitions of a cut-and-paste chain are 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 cut-and-paste chains, and under certain conditions on the distribution of the governing random matrices we show that the cutoff “phenomenon” holds.

MSC:

60J05 Discrete-time Markov processes on general state spaces
60B10 Convergence of probability measures
60B20 Random matrices (probabilistic aspects)
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