## Electronic Journal of Probability

### Random Walks on Trees and Matchings

#### 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.

#### Article information

Source
Electron. J. Probab., Volume 7 (2002), paper no. 6, 17 pp.

Dates
Accepted: 2 January 2002
First available in Project Euclid: 16 May 2016

https://projecteuclid.org/euclid.ejp/1463434879

Digital Object Identifier
doi:10.1214/EJP.v7-105

Mathematical Reviews number (MathSciNet)
MR1887626

Zentralblatt MATH identifier
1007.60071

Rights

#### Citation

Diaconis, Persi; Holmes, Susan. Random Walks on Trees and Matchings. Electron. J. Probab. 7 (2002), paper no. 6, 17 pp. doi:10.1214/EJP.v7-105. https://projecteuclid.org/euclid.ejp/1463434879

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