Subtree prune and regraft: a reversible real tree-valued Markov process
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 regraft (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.
Keywords
Cite
@article{arxiv.math/0502226,
title = {Subtree prune and regraft: a reversible real tree-valued Markov process},
author = {Steven N. Evans and Anita Winter},
journal= {arXiv preprint arXiv:math/0502226},
year = {2007}
}
Comments
Published at http://dx.doi.org/10.1214/009117906000000034 in the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org)