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CELEBRATING 50 YEARS OF THE APPLIED PROBABILITY TRUST

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 law of 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.