Götz Kersting, Juan Carlos Pardo, Arno Siri-Jégousse
Published 2013-02-06Version 1
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.
On the weak limit law of the maximal uniform k-spacing
A weak law of large numbers for realised covariation in a Hilbert space setting
A Spectral decomposition for the Bolthausen-Sznitman coalescent and the Kingman coalescent
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