@article{EJP2286,
author = {Jean-Stéphane Dhersin and Martin Möhle},
title = {On the external branches of coalescents with multiple collisions},
journal = {Electron. J. Probab.},
fjournal = {Electronic Journal of Probability},
volume = {18},
year = {2013},
keywords = {Asymptotic expansions; Bolthausen-Sznitman coalescent; external branches; joint moments; Kingman coalescent; multiple collisions},
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.},
pages = {no. 40, 1-11},
issn = {1083-6489},
doi = {10.1214/EJP.v18-2286},
url = {http://ejp.ejpecp.org/article/view/2286}}