Subtree prune and regraft: A reversible real tree-valued Markov process

• Steven N. Evans ^[1] ; Anita Winter ^[2]
  1. [1] University of California at Berkeley
  2. [2] Universität Erlangen-Nürnberg
• Localización: Annals of probability: An official journal of the Institute of Mathematical Statistics, ISSN 0091-1798, Vol. 34, Nº. 3, 2006, págs. 918-961
• Idioma: inglés
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• Resumen

  • 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.