PhD in universality in random trees and graphs (1.0 FTE)

Randomness and random shapes can be found everywhere around us, for example the shape of a tree is influenced by random interactions both between and within its cells, and random external influences. This random growth causes trees in nature to have self-similar, fractal-like properties. Underlying random growth also makes our backyard oak look remarkably similar to other structures in nature and systems of human design, such as the shape of river systems; the circulatory system in animals; and the connectivity structure of the internet and digital social networks. Broccolis looking like trees is a consequence of a universality principle in random structures: the precise random dynamics of cell growth in the two organisms is different, but those differences have a negligible effect on the overall structure.

The goal of this PhD project is to examine universality in random trees and graphs. (Morally, you will rigorously prove what it takes to look like a broccoli.) The focus will lie on directed graphs (in which edges have directions) and dynamical trees and graphs (in which the connectivity structure evolves over time). This research requires the PhD candidate to develop new combinatorial sampling methods, and to use techniques from (stochastic) analysis to study limiting properties. The PhD candidate will acquire skills that are broadly applicable in combinatorics and analysis, and in discrete and continuous probability theory.

The objective of the temporary position is the production of a number of research articles in peer-reviewed scientific journals and conference proceedings, which together will form the basis of a thesis leading to a PhD degree (Dr) at the University of Groningen. The position comes with a light teaching duty. The candidate will become a member of the Probability and Statistics Group of the Mathematics Department and will work under the supervision of Serte Donderwinkel.