Analytic and probabilistic tools for the study of random trees

The main goal of this project is to develop new tools for the study of random trees and related discrete structures.

In particular, we aim to develop general limit theorems that cover different models of randomness as well as different structural aspects.

Research on random trees is partly motivated by questions arising in other areas, such as phylogenetics and computer science.One specific goal is to develop general theorems to deal with infinite systems of functional equations for generating functions.

While the finite case is quite well understood, infinite systems are harder to deal with, and a systematic treatment is lacking. Such systems occur in the study of random trees, but also in other contexts.

A second goal is to develop new limit theorems for additive tree functionals and other general classes of tree functionals.Lastly, we investigate new models of random trees that we expect to exhibit unusual and interesting behaviour.

The most classical types of random tree models that have been studied extensively are trees of logarithmic height and trees of square root height.

Probabilistic models that can interpolate between these two worlds will allow us to observe new phenomena.The project links different parts of mathematics, especially enumerative combinatorics and probability theory, but real and complex analysis also play a significant role. Generating functions and analytic combinatorics are blended with probabilistic ingredients.