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Probability Workshop – TT2017

24 Apr 17

Speaker: Amaury Lambert, Laboratoire de Probabilités & Modèles Aléatoires, UPMC Univ Paris 06
Title: Random ultrametric trees and applications
Abstract: Ultrametric trees are trees whose leaves lie at the same distance from the root. They are used to model the genealogy of a population of particles co-existing at the same point in time. We show how the boundary of an ultrametric tree, like any compact ultrametric space, can be represented in a simple way via the so-called comb metric. We display a variety of examples of random combs and explain how they can be used in applications. In particular, we review some old and more recent results regarding the genetic structure of the population when throwing neutral mutations on the skeleton of the tree.