Asymptotic results on the length of coalescent trees

Asymptotic results on the length of coalescent trees

Jean-François Delmas, Jean-Stéphane Dhersin, and Arno Siri-Jegousse

Source: Ann. Appl. Probab. Volume 18, Number 3 (2008), 997-1025.

Abstract

We give the asymptotic distribution of the length of partial coalescent trees for Beta and related coalescents. This allows us to give the asymptotic distribution of the number of (neutral) mutations in the partial tree. This is a first step to study the asymptotic distribution of a natural estimator of DNA mutation rate for species with large families.

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Primary Subjects: 60F05, 60G52, 60J70, 05C05

Keywords: Coalescent process; Beta-coalescent; stable process; Watterson estimator

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Permanent link to this document: http://projecteuclid.org/euclid.aoap/1211819792
Digital Object Identifier: doi:10.1214/07-AAP476
Zentralblatt MATH identifier: 1141.60007
Mathematical Reviews number (MathSciNet): MR2418236

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