Vorträge in der Woche 16.01.2012 bis 22.01.2012

Montag, 16.01.2012: Coalescent trees and their symmetries

Prof. Dr. Götz Kersting

N-Coalescent trees describe the genealogy of N individuals chosen at random from a large population. Important quantities (from the point of view of applications) are their total length L(N) as well as their total external length E(N) , that is the total length of all branches ending in a leaf. In the talk we are concerned with the asymptotic distribution of these quantities. We shall address Kingman coalescents (which models the genealogy of a haploid population in equilibrium with random mating) as well as the larger class of Beta-coalescents. The results use hidden symmetries within these coalescents. Part of the talk builds on joint work with Svante Janson (Uppsala).