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arXiv · 2009.13642

The joint fluctuations of the lengths of the Beta$(2-α, α)$-coalescents

Matthias Birkner·Iulia Dahmer·Christina S. Diehl·Götz Kersting
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Abstract

We consider Beta$(2-α, α)$-coalescents with parameter range $1 <α<2$ starting from $n$ leaves. The length $\ell^{(n)}_r$ of order $r$ in the $n$-Beta$(2-α, α)$-coalescent tree is defined as the sum of the lengths of all branches that carry a subtree with $r$ leaves. We show that for any $s \in \mathbb N$ the vector of suitably centered and rescaled lengths of orders $1\le r \le s$ converges in distribution to a multivariate stable distribution as the number of leaves tends to infinity.

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Matthias Birkner, Iulia Dahmer, Christina S. Diehl, Götz Kersting. 2022-11-29. The joint fluctuations of the lengths of the Beta$(2-α, α)$-coalescents. https://arxiv.org/abs/2009.13642

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