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-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 DM12. An application to population genetics dealing with the total number of mutations in the genealogical tree is also given.
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