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Random Walks on Trees and Matchings


 
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1. Title Title of document Random Walks on Trees and Matchings
 
2. Creator Author's name, affiliation, country Persi Diaconis; Stanford University
 
2. Creator Author's name, affiliation, country Susan Holmes; Stanford University
 
3. Subject Discipline(s) Mathematics
 
3. Subject Keyword(s) Markov Chain, Matchings, Phylogenetic Tree, Fourier analysis, Zonal polynomials, Coagulation-Fragmentation.
 
3. Subject Subject classification 60J10 60B15 (60J10 62F10 62F15 65C05 82C80).
 
4. Description Abstract We give sharp rates of convergence for a natural Markov chain on the space of phylogenetic trees and dually for the natural random walk on the set of perfect matchings in the complete graph on $2n$ vertices. Roughly, the results show that $(1/2) n \log n$ steps are necessary and suffice to achieve randomness. The proof depends on the representation theory of the symmetric group and a bijection between trees and matchings.
 
5. Publisher Organizing agency, location
 
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7. Date (YYYY-MM-DD) 2002-01-02
 
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/105
 
10. Identifier Digital Object Identifier 10.1214/EJP.v7-105
 
11. Source Journal/conference title; vol., no. (year) Electronic Journal of Probability; Vol 7
 
12. Language English=en en
 
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