External branch lengths of $\Lambda $-coalescents without a dust component

@article{Diehl2019ExternalBL,
  title={External branch lengths of \$\Lambda \$-coalescents without a dust component},
  author={Christina S. Diehl and G{\"o}tz Kersting},
  journal={Electronic Journal of Probability},
  year={2019}
}
$\Lambda$-coalescents model genealogies of samples of individuals from a large population by means of a family tree whose branches have lengths. The tree's leaves represent the individuals, and the lengths of the adjacent edges indicate the individuals' time durations up to some common ancestor. These edges are called external branches. We consider typical external branches under the broad assumption that the coalescent has no dust component, and maximal external branches under further… 

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References

SHOWING 1-10 OF 40 REFERENCES
Tree lengths for general $\Lambda $-coalescents and the asymptotic site frequency spectrum around the Bolthausen–Sznitman coalescent
We study tree lengths in $\Lambda$-coalescents without a dust component from a sample of $n$ individuals. For the total lengths of all branches and the total lengths of all external branches we
Minimal clade size and external branch length under the neutral coalescent
Given a sample of genes taken from a large population, we consider the neutral coalescent genealogy and study the theoretical and empirical distributions of the size of the smallest clade containing
The size of the last merger and time reversal in $\Lambda$-coalescents
Author(s): Kersting, Goetz; Schweinsberg, Jason; Wakolbinger, Anton | Abstract: We consider the number of blocks involved in the last merger of a $\Lambda$-coalescent started with $n$ blocks. We give
Can the Site-Frequency Spectrum Distinguish Exponential Population Growth from Multiple-Merger Coalescents?
TLDR
Estimates of statistical power indicate that exponential and algebraic growth can indeed be distinguished from multiple-merger coalescents, even for moderate sample sizes, if the number of segregating sites is high enough.
The evolving beta coalescent
In mathematical population genetics, it is well known that one can represent the genealogy of a population by a tree, which indicates how the ancestral lines of individuals in the population coalesce
The Total External Branch Length of Beta-Coalescents†
TLDR
It turns out that the fluctuations of the external branch length follow those of τn2−α over the entire parameter regime, where τn denotes the random number of coalescences that bring the n lineages down to one.
The general coalescent with asynchronous mergers of ancestral lines
Take a sample of individuals in the fixed-size population model with exchangeable family sizes. Follow the ancestral lines for the sampled individuals backwards in time to observe the ancestral
Rigorous results for a population model with selection II: genealogy of the population
We consider a model of a population of fixed size $N$ undergoing selection. Each individual acquires beneficial mutations at rate $\mu_N$, and each beneficial mutation increases the individual's
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