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| HAL : hal-00732541, version 3 |
| arXiv : 1209.3380 |
| Fiche détaillée |  Récupérer au format |
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| Versions disponibles : | v1 (15-09-2012) | v2 (24-01-2013) | v3 (24-02-2013) |
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| On the external branches of coalescents with multiple collisions |
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Jean-Stephane Dhersin 1, 2Martin Moehle 3 |
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| (30/08/2012) |
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| 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 $n\ge 4$. |
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| 1 : | Institut Galilée (IG) |
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Université Paris XIII - Paris Nord |
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| 2 : | Laboratoire Analyse, Géométrie et Application (LAGA) |
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CNRS : UMR7539 – Université Paris XIII - Paris Nord – Université Paris VIII - Vincennes Saint-Denis |
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| 3 : | Mathematisches Institut |
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Tübingen Universität - Tübingen University |
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| Stochastics Group - Mathematical Institute - University of Tübingen |
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| Domaine | : | Mathématiques/Probabilités Sciences du Vivant/Génétique/Génétique des populations |
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| Asymptotic expansions – Bolthausen-Sznitman coalescent – external branches – joint moments – Kingman coalescent – multiple collisions. |
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| hal-00732541, version 3 | |
| http://hal.archives-ouvertes.fr/hal-00732541 | |
| oai:hal.archives-ouvertes.fr:hal-00732541 | |
| Contributeur : Jean-Stephane Dhersin | |
| Soumis le : Dimanche 24 Février 2013, 13:43:31 | |
| Dernière modification le : Dimanche 24 Février 2013, 13:58:05 | |
