@article{EJP105,
author = {Persi Diaconis and Susan Holmes},
title = {Random Walks on Trees and Matchings},
journal = {Electron. J. Probab.},
fjournal = {Electronic Journal of Probability},
volume = {7},
year = {2002},
keywords = {Markov Chain, Matchings, Phylogenetic Tree, Fourier analysis, Zonal polynomials, Coagulation-Fragmentation.},
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.},
pages = {no. 6, 1-17},
issn = {1083-6489},
doi = {10.1214/EJP.v7-105},
url = {http://ejp.ejpecp.org/article/view/105}}