• Corpus ID: 16792134

Asympotic behavior of the total length of external branches for Beta-coalescents

@article{Dhersin2012AsympoticBO,
  title={Asympotic behavior of the total length of external branches for Beta-coalescents},
  author={J. S. Dhersin and Linglong Yuan},
  journal={arXiv: Probability},
  year={2012}
}
We consider a ${\Lambda}$-coalescent and we study the asymptotic behavior of the total length $L^{(n)}_{ext}$ of the external branches of the associated $n$-coalescent. For Kingman coalescent, i.e. ${\Lambda}={\delta}_0$, the result is well known and is useful, together with the total length $L^{(n)}$, for Fu and Li's test of neutrality of mutations% under the infinite sites model asumption . For a large family of measures ${\Lambda}$, including Beta$(2-{\alpha},{\alpha})$ with $0<\alpha<1$, M… 

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