The Aldous chain on cladograms in the diffusion limit

DOI10.1214/20-AOP1431zbMath1452.60045arXiv1805.12057MaRDI QIDQ2212602

Anita Winter, Wolfgang Löhr, Leonid Mytnik

Publication date: 24 November 2020

Published in: The Annals of Probability (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1805.12057

zbMATH Keywords

martingale problemWright-Fisher diffusionalgebraic treescontinuum treeGromov-weak convergencesample shape convergencetree-valued diffusiontree-valued Markov chain

Mathematics Subject Classification ID

Continuous-time Markov processes on general state spaces (60J25) Diffusion processes (60J60) Branching processes (Galton-Watson, birth-and-death, etc.) (60J80)

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Cites Work

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• Doob-Martin boundary of Rémy's tree growth chain
• Equivalence of Gromov-Prohorov- and Gromov's \(\underline{\square}_\lambda\)-metric on the space of metric measure spaces
• Convergence in distribution of random metric measure spaces (\(\Lambda \)-coalescent measure trees)
• Convergence of bi-measure \(\mathbb{R}\)-trees and the pruning process
• Recursive self-similarity for random trees, random triangulations and Brownian excursion
• Geometry of the space of phylogenetic trees
• Uniform control of local times of spectrally positive stable processes
• Landscapes on spaces of trees
• Tree-valued Fleming-Viot dynamics with mutation and selection
• Tree-valued resampling dynamics martingale problems and applications
• The continuum random tree. III
• Invariance principle for variable speed random walks on trees
• Subtree prune and regraft: a reversible real tree-valued Markov process
• Existence of mark functions in marked metric measure spaces
• Mixing Time for a Markov Chain on Cladograms
• Subtree transfer operations and their induced metrics on evolutionary trees