The present paper is a brief survey of properties of finite ultrametric spaces X and
corresponding properties of the representing trees TX obtained by authors over the last six …

Consider a continuous-state branching population constructed as a flow of nested
subordinators. Inverting the subordinators and reversing time give rise to a flow of …

We consider single attractive facility location problems of general kind, with distance
measured by an ultrametric. We show that the set of destinations always contains an (and …

We investigate compact ultrametric measure spaces which form a subset U w of the
collection of all metric measure spaces M w. In analogy with the notion of the ultrametric …

The goal of these lectures is to review some mathematical aspects of random tree models
used in evolutionary biology to model species trees. We start with stochastic models of tree …

We investigate the interrelations between labeled trees and ultrametric spaces generated by
these trees. The labeled trees, which generate complete ultrametrics, totally bounded …

Kingman's (1978) representation theorem (J. Lond. Math. Soc.(2) 18 (1978) 374–380) states
that any exchangeable partition of ℕ can be represented as a paintbox based on a random …

We consider a general class of branching processes in discrete time, where particles have
types belonging to a Polish space and reproduce independently according to their type. If …

Consider a random real tree whose leaf set, or boundary, is endowed with a finite mass
measure. Each element of the tree is further given a type, or allele, inherited from the most …

We consider a continuous population whose dynamics is described by the standard
stationary Fleming–Viot process, so that the genealogy of n uniformly sampled individuals is …