Title: Subtree prune and re-graft: a reversible real tree valued Markov process
Author: Steven N. Evans and Anita Winter
pub: PDF
Url: http://www.stat.berkeley.edu/users/evans/685.pdf
Date: February 2005
Abstract: We use Dirichlet form methods to construct and analyze
a reversible Markov process, the stationary distribution of
which is the Brownian continuum random tree.  This process is
inspired by the subtree prune and re-graft (SPR) Markov chains
that appear in phylogenetic analysis.
A key technical ingredient in this work is the use of a novel
Gromov--Hausdorff type distance to metrize the space whose
elements are compact real trees equipped with a probability
measure.  Also, the investigation of the Dirichlet form hinges
on a new path decomposition of the Brownian excursion.