Asymptotic results on the length of coalescent trees

Jean-François Delmas (1) , Jean-Stéphane Dhersin (2) , Arno Siri-Jegousse (2)

1 CERMICS - Centre d'Enseignement et de Recherche en Mathématiques, Informatique et Calcul Scientifique
2 MAP5 - UMR 8145 - Mathématiques Appliquées Paris 5

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.

Mots clés: Coalescent process; Beta-coalescent; stable process; Watterson estimator

Domaines: Probabilités [math.PR]

Jean-François Delmas, Jean-Stéphane Dhersin, Arno Siri-Jegousse. Asymptotic results on the length of coalescent trees. 2007. ⟨hal-00151205⟩