Convergence Rates of Markov Chains on Spaces of Partitions

2012/09/21 by Harry Crane, Crane, Harry, Steven P. Lalley +1
Mathematics · #60J05 #FOS: Mathematics #Markov Chains and Monte Carlo Methods #Mathematical Dynamics and Fractals #Probability (math.PR) #Stochastic processes and statistical mechanics #math.PR #msc:60J05

paper · pdf · doi:10.48550/arxiv.1209.4918

arxiv created 2012/09/21 · openalex publication_date 2012/09/21 · arxiv updated 2012/09/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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.

Citations

• Products of Random Matrices

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