| Título: | On the external branches of coalescents with multiple collisions |
| Autores: |
Dhersin, Jean-Stéphane; Sorbonne Paris Cité Möhle, Martin; Eberhard Karls Universität Tübingen |
| Fecha: | 2013-01-04 |
| Publicador: | Electronic journal of probability |
| Fuente: |
 |
| Tipo: | Peer-reviewed Article |
| Tema: |
Asymptotic expansions; Bolthausen-Sznitman coalescent; external branches; joint moments; Kingman coalescent; multiple collisions 60J25; 34E05; 60C05; 60J85; 92D15; 92D25 |
| Descripción: | A recursion for the joint moments of the external branch lengths for coalescents with multiple collisions (Lambda-coalescents) is provided. This recursion is used to derive asymptotic results as the sample size n tends to infinity for the joint moments of the external branch lengths and for the moments of the total external branch length of the Bolthausen-Sznitman coalescent. These asymptotic results are based on a differential equation approach, which is as well useful to obtain exact solutions for the joint moments of the external branch lengths for the Bolthausen-Sznitman coalescent. The results for example show that the lengths of two randomly chosen external branches are positively correlated for the Bolthausen-Sznitman coalescent, whereas they are negatively correlated for the Kingman coalescent provided that n >= 4. |
| Idioma: | Inglés |
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