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

rug university groningen
  • Groningen
  • University of Groningen
Posted on

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.


The successful candidate should

  • have a master’s degree or equivalent in mathematics or another relevant field with sufficient mathematical content; preferably with a focus on combinatorics or probability theory
  • have good English language and communication skills.

Conditions of employment

We offer you, following the Collective Labour Agreement for Dutch Universities

  • a salary of € 2,770 gross per month in the first year, up to a maximum of € 3,539 gross per month in the fourth and final year for a full-time working week
  • a holiday allowance of 8% gross annual income and an 8.3% year-end bonus
  • a full-time position (1.0 FTE).

The successful candidate will first be offered a temporary position of one year with the option of renewal for another three years. Prolongation of the contract is contingent on sufficient progress in the first year to indicate that a successful completion of the PhD thesis within the next three years is to be expected. A PhD training programme is part of the agreement and the successful candidate will be enrolled in the Graduate School of Science and Engineering.

Preferred starting date: September 1 (or in consultation with the candidate)


Application should include

  • a cover letter describing your background and motivation (max 1 page)
  • a CV
  • transcripts from your bachelor’s and master’s degree (or a list of grades/proof of enrolment if you are near finishing)
  • a letter of recommendation that should be sent directly to (please mention your reference letter writer in your cover letter).

You may apply for this position until 14 May 11:59pm / before 15 May 2024 Dutch local time (CEST) by means of the application form (click on "Apply" below on the advertisement on the university website).

Applications received before 14 May 2023 will be given full consideration; however, the position will remain open until it is filled.


For information you can contact:

Please do not use the e-mail address(es) above for applications.

Ole Gmelin

"Speaking Dutch in the Netherlands will always open certain doors for you when it comes to finding a job. But, it isn’t always a must."

Will you become our new PhD in universality in random trees and graphs (1.0 FTE)? Apply at University of Groningen