Total internal and external lengths of the Bolthausen-Sznitman coalescent

Abstract

In this paper we study a weak law of large numbers for the total internal length of the Bolthausen-Sznitman coalescent, thereby obtaining the weak limit lawof the centered and rescaled total external length; this extends results obtained in Dhersin and Möhle (2013). An application to population genetics dealing with the total number of mutations in the genealogical tree is also given.