The total external length of the evolving Kingman coalescent

DOI10.1007/s00440-016-0703-7zbMath1373.60154arXiv1412.6635OpenAlexW2963448822MaRDI QIDQ525109

Iulia Dahmer, Götz-Dietrich Kersting

Publication date: 28 April 2017

Published in: Probability Theory and Related Fields (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1412.6635

zbMATH Keywords

Gaussian processcentral limit theoremcouplingcritical branching processevolving Kingman coalescentexternal length process

Mathematics Subject Classification ID

Central limit and other weak theorems (60F05) Interacting random processes; statistical mechanics type models; percolation theory (60K35) Population dynamics (general) (92D25) Branching processes (Galton-Watson, birth-and-death, etc.) (60J80)

Related Items

A compendium of covariances and correlation coefficients of coalescent tree properties ⋮ A representation for exchangeable coalescent trees and generalized tree-valued Fleming-Viot processes ⋮ Pathwise construction of tree-valued Fleming-Viot processes ⋮ On the joint distribution of tree height and tree length under the coalescent

Cites Work

• Unnamed Item
• Unnamed Item
• Asymptotic sampling formulae for \(\varLambda\)-coalescents
• On the total external length of the Kingman coalescent
• Dynamics of the evolving Bolthausen-Sznitman coalescent
• Asymptotic results for coalescent processes without proper frequencies and applications to the two-parameter Poisson-Dirichlet coalescent
• The tree length of an evolving coalescent
• The asymptotic distribution of the length of beta-coalescent trees
• Small-time behavior of beta coalescents
• The evolving beta coalescent
• Convergence in distribution of random metric measure spaces (\(\Lambda \)-coalescent measure trees)
• The process of most recent common ancestors in an evolving coalescent
• A representation for exchangeable coalescent trees and generalized tree-valued Fleming-Viot processes
• Statistical properties of segregating sites
• Tree-valued Fleming-Viot dynamics with mutation and selection
• Tree-valued resampling dynamics martingale problems and applications
• The internal branch lengths of the Kingman coalescent
• Asymptotic results concerning the total branch length of the Bolthausen-Sznitman coalescent
• Beta-coalescents and continuous stable random trees
• A probabilistic proof of a weak limit law for the number of cuts needed to isolate the root of a random recursive tree
• The Kingman tree length process has infinite quadratic variation
• The Total External Branch Length of Beta-Coalescents
• On the total length of external branches for beta-coalescents
• Probability Models for DNA Sequence Evolution
• Markov Processes, Gaussian Processes, and Local Times