On Asymptotics of the Beta Coalescents

DOI10.1239/aap/1401369704zbMath1323.60021arXiv1203.3110OpenAlexW2069398968MaRDI QIDQ5169504

Alexander Marynych, Martin Möhle, Alexander V. Gnedin, Aleksander M. Iksanov

Publication date: 10 July 2014

Published in: Advances in Applied Probability (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1203.3110

zbMATH Keywords

asymptotic expansioncouplingWasserstein distanceabsorption timetotal branch lengthnumber of collisionsbeta coalescent

Mathematics Subject Classification ID

Central limit and other weak theorems (60F05) Markov chains (discrete-time Markov processes on discrete state spaces) (60J10) Combinatorial probability (60C05) Exchangeability for stochastic processes (60G09)

Related Items (5)

The collision spectrum of \(\Lambda\)-coalescents ⋮ The joint fluctuations of the lengths of the \(\operatorname{Beta}(2 - {\alpha}, {\alpha})\)-coalescents ⋮ A spectral decomposition for the block counting process and the fixation line of the beta(3,1)-coalescent ⋮ The fixation line in the \(\Lambda\)-coalescent ⋮ Λ-coalescents: a survey

Cites Work

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• On the number of collisions in beta(\(2, b\))-coalescents
• Asymptotic results for coalescent processes without proper frequencies and applications to the two-parameter Poisson-Dirichlet coalescent
• Self-similar scaling limits of non-increasing Markov chains
• The asymptotic distribution of the length of beta-coalescent trees
• On the extended Moran model and its relation to coalescents with multiple collisions
• Central limit theorem and convergence to stable laws in Mallows distance
• Random recursive trees and the Bolthausen-Sznitman coalescent
• Asymptotic results on the length of coalescent trees
• On the number of collisions in lambda-coalescents
• A class of Wasserstein metrics for probability distributions
• The coalescent
• On Ruelle's probability cascades and an abstract cavity method
• Coalescents with multiple collisions
• The Bolthausen-Sznitman coalescent and the genealogy of continuous-state branching processes
• Alpha-stable branching and beta-coalescents
• Two coalescents derived from the ranges of stable subordinators
• 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
• A probabilistic proof of a weak limit law for the number of cuts needed to isolate the root of a random recursive tree
• On Λ-Coalescents with Dust Component
• Recent progress in coalescent theory
• A limiting distribution for the number of cuts needed to isolate the root of a random recursive tree
• The general coalescent with asynchronous mergers of ancestral lines
• On the number of jumps of random walks with a barrier
• On the number of segregating sites for populations with large family sizes
• On Asymptotics of Exchangeable Coalescents with Multiple Collisions
• Fluctuation Theory of Recurrent Events

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