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arXiv · 1302.1463

Total internal and external lengths of the Bolthausen-Sznitman coalescent

Götz Kersting·Juan Carlos Pardo·Arno Siri-Jégousse
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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 \cite{DM12}. An application to population genetics dealing with the total number of mutations in the genealogical tree is also given.

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Götz Kersting, Juan Carlos Pardo, Arno Siri-Jégousse. 2013-02-06. Total internal and external lengths of the Bolthausen-Sznitman coalescent. https://arxiv.org/abs/1302.1463

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