Corpus ID: 221995574

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

@article{Birkner2020TheJF,
  title={The joint fluctuations of the lengths of the Beta\$(2-\alpha, \alpha)\$-coalescents},
  author={M. Birkner and Iulia Dahmer and Christina S. Diehl and G. Kersting},
  journal={arXiv: Probability},
  year={2020}
}
We consider Beta$(2-\alpha, \alpha)-n$-coalescents with parameter range $1 <\alpha<2$. The length $\ell^{(n)}_r$ of order $r$ in the Beta$(2-\alpha, \alpha)-n$-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 (as the number of leaves tends to infinity) to a multivariate stable distribution. 

References

SHOWING 1-10 OF 26 REFERENCES
The Total External Branch Length of Beta-Coalescents†
On the total length of external branches for beta-coalescents
...
1
2
3
...