Open Access
2013 Convergence rates of Markov chains on spaces of partitions
Harry Crane, Steven Lalley
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Electron. J. Probab. 18: 1-23 (2013). DOI: 10.1214/EJP.v18-2389


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.


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Harry Crane. Steven Lalley. "Convergence rates of Markov chains on spaces of partitions." Electron. J. Probab. 18 1 - 23, 2013.


Accepted: 13 June 2013; Published: 2013
First available in Project Euclid: 4 June 2016

zbMATH: 1296.60183
MathSciNet: MR3078020
Digital Object Identifier: 10.1214/EJP.v18-2389

Primary: 60J05
Secondary: 60B10 , 60B20

Keywords: cut-and-paste chain , Cutoff phenomenon , exchangeability , Lyapunov exponent , mixing time

Vol.18 • 2013
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