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

@article{Diehl2019TreeLF,
  title={Tree lengths for general \$\Lambda \$-coalescents and the asymptotic site frequency spectrum around the Bolthausen–Sznitman coalescent},
  author={Christina S. Diehl and G{\"o}tz Kersting},
  journal={The Annals of Applied Probability},
  year={2019}
}
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 present laws of large numbers in full generality. The other results treat regulary varying coalescents with exponent 1, which cover the Bolthausen-Sznitman coalescent. The theorems contain laws of large numbers for the total lengths of all internal branches and of internal branches of order $a$ (i.e… 
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J an 2 02 2 The joint fluctuations of the lengths of the Beta ( 2 − α , α )-coalescents ∗
We consider Beta(2− α, α)-coalescents with parameter range 1 < α < 2 starting from n leaves. The length l (n) r of order r in the n-Beta(2 − α, α)-coalescent tree is defined as the sum of the lengths
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