Research

Articles and preprints

Continuum asymptotics for tree growth models arXiv [2309.04336]

Abstract: We classify the forward dynamics of all (plane) tree-valued Markov chains $(T_n,n\geq 1)$ with uniform backward dynamics. Every such Markov chain is classified by a decorated planar real tree. We also show that under an inhomogeneous rescaling after trimming leaves $(T_n,n\geq 1)$ converges to a random real tree in the Gromov-Prokhorov metric. This generalises and sheds some new light on work by Evans, Grübel and Wakolbinger (2017) on the binary special case.

Current projects

Branching growth on trees Here we consider a branching random walk on a supercritical Galton-Watson tree. This is an example for a stochastic process in a random environment. The goal is to determine the invasion speed, this is the speed at which the process occupies the environment, as well as the speed of saturation.

Spacially inhomogeneous branching Brownian motion (with Michel Pain and Julien Berestycki) Here we consider a two-dimensional branching Brownian motion where the branching rate depends on the angle of a particle towards the origin. The goal is to deterine the exact speed of the maximal particle, i.e. the particle at the greatest distance to the origin.

Old theses

Here are my old theses as pdfs:

Bachelor thesis: The Scaling Limit of the Erdös-Rény Graph

Master thesis: Ergodicity of the dynamical XY-model