A survey on the asymptotic behavior of beta coalescents

What is it about?

This article summaries known limiting results on certain functionals of beta n-coalescents when the sample size n tends to infinity with an emphasis on the number of collisions, the absorption time and the total branch length of the coalescent. The new part of the article concerns the beta(1,b)-coalescent with arbitrary parameter b>0. The quality of a renewal approximation to the coalescent is estimated in terms of a suitable Wasserstein distance.

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