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On the external branches of coalescents with multiple collisions

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1.	Title	Title of document	On the external branches of coalescents with multiple collisions
2.	Creator	Author's name, affiliation, country	Jean-Stéphane Dhersin; Sorbonne Paris Cité; France
2.	Creator	Author's name, affiliation, country	Martin Möhle; Eberhard Karls Universität Tübingen; Germany
3.	Subject	Discipline(s)
3.	Subject	Keyword(s)	Asymptotic expansions; Bolthausen-Sznitman coalescent; external branches; joint moments; Kingman coalescent; multiple collisions
3.	Subject	Subject classification	60J25; 34E05; 60C05; 60J85; 92D15; 92D25
4.	Description	Abstract	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.
5.	Publisher	Organizing agency, location
6.	Contributor	Sponsor(s)
7.	Date	(YYYY-MM-DD)	2013-03-20
8.	Type	Status & genre	Peer-reviewed Article
8.	Type	Type
9.	Format	File format	PDF
10.	Identifier	Uniform Resource Identifier	http://ejp.ejpecp.org/article/view/2286
10.	Identifier	Digital Object Identifier	10.1214/EJP.v18-2286
11.	Source	Journal/conference title; vol., no. (year)	Electronic Journal of Probability; Vol 18
12.	Language	English=en	en
14.	Coverage	Geo-spatial location, chronological period, research sample (gender, age, etc.)
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