Random Walks on Trees and Matchings
Persi Diaconis, Stanford University
Susan Holmes, Stanford University
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.
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