2005/02/28 by Steven N. Evans, Anita Winter · 1 citation
Biochemistry, Genetics and Molecular Biology · Mathematics · Physics and Astronomy · #Complex Network Analysis Techniques #Markov Chains and Monte Carlo Methods #Stochastic processes and statistical mechanics #math.MG #math.PR #msc:60J25 #msc:60J75 #msc:92B10 #q-bio.PE #q-bio.QM
paper · pdf · doi:10.1214/009117906000000034
published as Annals of Probability 2006, Vol. 34, No. 3, 918-961 · 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)
openalex publication_date 2006/05/01 · arxiv created 2006/06/29 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
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.