Total internal and external lengths of the Bolthausen-Sznitman coalescent
Götz Kersting, Juan Carlos Pardo, Arno Siri-Jégousse
(Submitted on 6 Feb 2013)

In this paper, we study a weak law of large numbers for the total internal length of the Bolthausen-Szmitman coalescent. As a consequence, we obtain the weak limit law of the centered and rescaled total external length. The latter extends results obtained by Dhersin & M\”ohle \cite{DM12}. An application to population genetics dealing with the total number of mutations in the genealogical tree is also given.