Tree lengths for general \(\Lambda \)-coalescents and the asymptotic site frequency spectrum around the Bolthausen-Sznitman coalescent

DOI10.1214/19-AAP1462zbMath1475.60159arXiv1804.00961OpenAlexW2981025968MaRDI QIDQ2286448

Christina S. Diehl, Götz-Dietrich Kersting

Publication date: 22 January 2020

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

Full work available at URL: https://arxiv.org/abs/1804.00961

zbMATH Keywords

law of large numberssite frequency spectrumBolthausen-Sznitman coalescentsampling formulainfinite sites modeltree length\( \Lambda \)-coalescentdecreasing Markov chain

Mathematics Subject Classification ID

Central limit and other weak theorems (60F05) Population dynamics (general) (92D25) Continuous-time Markov processes on discrete state spaces (60J27) Jump processes on discrete state spaces (60J74) Coalescent processes (60J90)

Related Items (7)

Site Frequency Spectrum of the Bolthausen-Sznitman Coalescent ⋮ Scaling limits for a class of regular \(\Xi\)-coalescents ⋮ The joint fluctuations of the lengths of the \(\operatorname{Beta}(2 - {\alpha}, {\alpha})\)-coalescents ⋮ Asymptotics of the frequency spectrum for general Dirichlet \(\Xi\)-coalescents ⋮ Population dynamics and statistical physics in synergy. Abstracts from the workshop held March 6--12, 2022 ⋮ External branch lengths of \(\Lambda \)-coalescents without a dust component ⋮ The shape of a seed bank tree

Cites Work

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• On the external branches of coalescents with multiple collisions
• Asymptotic sampling formulae for \(\varLambda\)-coalescents
• On the total external length of the Kingman coalescent
• Asymptotic results for coalescent processes without proper frequencies and applications to the two-parameter Poisson-Dirichlet coalescent
• The asymptotic distribution of the length of beta-coalescent trees
• The evolving beta coalescent
• Random recursive trees and the Bolthausen-Sznitman coalescent
• Asymptotic results on the length of coalescent trees
• Asymptotics of the allele frequency spectrum associated with the Bolthausen-Sznitman coalescent
• On the number of segregating sites in genetical models without recombination
• On Ruelle's probability cascades and an abstract cavity method
• Coalescents with multiple collisions
• A necessary and sufficient condition for the \(\Lambda\)-coalescent to come down from the infinity
• Asymptotic results concerning the total branch length of the Bolthausen-Sznitman coalescent
• Beta-coalescents and continuous stable random trees
• Recent progress in coalescent theory
• The general coalescent with asynchronous mergers of ancestral lines
• Total internal and external lengths of the Bolthausen-Sznitman coalescent

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