Geodesic
Random ultrametric trees and applications
Amaury Lambert1
1 Université Pierre et Marie Curie – UPMC Univ Paris 06, Laboratoire de Probabilités et Modèles Aléatoires, Case 188, 4 place Jussieu, 75252 PARIS Cedex 05; email:
ESAIM. Proceedings, Tome 60 (2017), pp. 70-89.

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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 recent results regarding the genetic structure of the population when throwing neutral mutations on the skeleton of the tree.
DOI : 10.1051/proc/201760070

Amaury Lambert 1

1 Université Pierre et Marie Curie – UPMC Univ Paris 06, Laboratoire de Probabilités et Modèles Aléatoires, Case 188, 4 place Jussieu, 75252 PARIS Cedex 05; email: 
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Amaury Lambert. Random ultrametric trees and applications. ESAIM. Proceedings, Tome 60 (2017), pp. 70-89. doi : 10.1051/proc/201760070. http://geodesic.mathdoc.fr/articles/10.1051/proc/201760070/

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