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Convergence rates of Markov chains on spaces of partitions


 
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1. Title Title of document Convergence rates of Markov chains on spaces of partitions
 
2. Creator Author's name, affiliation, country Harry Crane; Rutgers University; United States
 
2. Creator Author's name, affiliation, country Steven P. Lalley; University of Chicago; United States
 
3. Subject Discipline(s)
 
3. Subject Keyword(s) cut-and-paste chain; mixing time; exchangeability; cutoff phenomenon; Lyapunov exponent
 
3. Subject Subject classification Primary 60J05; secondary 60B10 60B20
 
4. Description 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.
 
5. Publisher Organizing agency, location
 
6. Contributor Sponsor(s) NSF
 
7. Date (YYYY-MM-DD) 2013-06-13
 
8. Type Status & genre Peer-reviewed Article
 
8. Type Type
 
9. Format File format PDF
 
10. Identifier Uniform Resource Identifier http://ejp.ejpecp.org/article/view/2389
 
10. Identifier Digital Object Identifier 10.1214/EJP.v18-2389
 
11. Source Journal/conference title; vol., no. (year) Electronic Journal of Probability; Vol 18
 
12. Language English=en en
 
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