Total internal and external lengths of the Bolthausen-Sznitman coalescent

2013/02/06 by Götz Kersting, Kersting, Götz, Juan Carlos Pardo +4
Biochemistry, Genetics and Molecular Biology · Mathematics · #Evolution and Genetic Dynamics #FOS: Biological sciences #FOS: Mathematics #Mathematical Dynamics and Fractals #Populations and Evolution (q-bio.PE) #Probability (math.PR) #Stochastic processes and statistical mechanics #math.PR #q-bio.PE

paper · pdf · doi:10.48550/arxiv.1302.1463

arxiv created 2013/02/06 · openalex publication_date 2013/02/06 · arxiv updated 2013/02/07 · openalex created_date 2022/10/04 · openalex updated_date 2026/07/28

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 & Möhle \citeDM12. An application to population genetics dealing with the total number of mutations in the genealogical tree is also given.

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