Coalescent theory is the study of random processes where particles may join each other to
form clusters as time evolves. These notes provide an introduction to some aspects of the …

The present book offers a detailed treatment of perturbed random walks, perpetuities, and
random processes with immigration. These objects are of major importance in modern …

Small-time behavior of beta coalescents Page 1 www.imstat.org/aihp Annales de l’Institut Henri
Poincaré - Probabilités et Statistiques 2008, Vol. 44, No. 2, 214–238 DOI: 10.1214/07-AIHP103 …

The genealogical structure of neutral populations in which reproductive success is highly-
skewed has been the subject of many recent studies. Here we derive a coalescent dual …

We study the total branch length Ln of the Bolthausen–Sznitman coalescent as the sample
size n tends to infinity. Asymptotic expansions for the moments of Ln are presented. It is …

We review recent progress in the understanding of the interplay between population models,
measure-valued diffusions, general coalescent processes and inference methods for …

The class of coalescent processes with simultaneous multiple collisions (Ξ-coalescents)
without proper frequencies is considered. We study the asymptotic behavior of the external …

Modeling genetic diversity needs an underlying genealogy model. To choose a fitting model
based on genetic data, one can perform model selection between classes of genealogical …

We present a robust method which translates information on the speed of coming down from
infinity of a genealogical tree into sampling formulae for the underlying population. We apply …

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 …