The theory of branching processes is an area of mathematics that describes situations in
which an entity exists for a time and then may be replaced by one, two, or more entities of a …

Take a continuous-time Galton–Watson tree. If the system survives until a large time T, then
choose k particles uniformly from those alive. What does the ancestral tree drawn out by …

Consider a branching Markov process with values in some general type space. Conditional
on survival up to generation N, the genealogy of the extant population defines a random …

We are interested in the dynamic of a structured branching population where the trait of each
individual moves according to a Markov process. The rate of division of each individual is a …

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 …

Problems in engineering, computational science, and the physical and biological sciences
are using increasingly sophisticated mathematical techniques. Thus, the bridge between the …

Building on the spinal decomposition technique in Foutel-Rodier and Schertzer (2022) we
prove a Yaglom limit law for the rescaled size of a nearly critical branching process in …

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 distribution of the coalescence time (most recent common ancestor) for
two individuals picked at random (uniformly) in the current generation of a continuous-time …

We introduce a Poissonization method to study the coalescent structure of uniform samples
from branching processes. This method relies on the simple observation that a uniform …