Lattice models from statistical mechanics have been successfully used in biology, information and social sciences to describe macroscopic properties of interacting systems by specifying their random microscopic interaction. To understand critical phenomena it is desirable to classify together models with the same macroscopic behavior: these categories are known in physics as universality classes. They are extremely useful for predictions, but they carry with them a major challenge: they are represented not by random variables, but by random generalised functions or random distributions. More notably, the representants can be functions of random distributions, making their definition completely formal and far from mathematically rigorous.

The research work lies in the intersection of the area of theoretical probability, analysis and distribution theory. The PhD project aims at understanding a long-standing question in analysis and probability, namely how to define functions of (random) distributions. In particular we will construct functions of random distribution using suitable discrete models and we plan to investigate the­ limits of physical systems in different geometries as well.

As a PhD student your task is to: 

• study relevant literature and learn the necessary mathematical techniques in order to tackle the problems mentioned above,
• present results on scientific conferences,
• attend research seminars, local at TU Delft or University of Utrecht and the national Mark Kac seminar,
• publish articles in renowned scientific journals,
• participate in the activities of the project team involving PhD students and PostDocs,
• do modest teaching duties at TU Delft.

This project is a joint collaboration between Dr. Cipriani from the Department of Applied Mathematics at TU Delft and Dr. Ruszel from the Mathematics Institute of Utrecht University. The candidate will be based at TU Delft but regularly visit Utrecht University. For more information about the research interests of the supervisors please visit https://sites.google.com/site/aciprian41/ and https://www.uu.nl/staff/WMRuszel.

1. A MSc degree in mathematics with specialisation in the area of theoretical probability or analysis.
2. Good communication skills both in written and spoken English.

Fixed-term contract: 4 years.

TU Delft offers a customisable compensation package, a discount for health insurance and sport memberships, and a monthly work costs contribution. Flexible work schedules can be arranged. An International Children’s Centre offers childcare and an international primary school. Dual Career Services offers support to accompanying partners. Salary and benefits are in accordance with the Collective Labour Agreement for Dutch Universities.
As a PhD candidate you will be enrolled in the TU Delft Graduate School. TU Delft Graduate School provides an inspiring research environment; an excellent team of supervisors, academic staff and a mentor; and a Doctoral Education Programme aimed at developing your transferable, discipline-related and research skills. Please visit www.tudelft.nl/phd for more information.

Technische Universiteit Delft

Delft University of Technology (TU Delft) is a multifaceted institution offering education and carrying out research in the technical sciences at an internationally recognised level. Education, research and design are strongly oriented towards applicability. TU Delft develops technologies for future generations, focusing on sustainability, safety and economic vitality. At TU Delft you will work in an environment where technical sciences and society converge. TU Delft comprises eight faculties, unique laboratories, research institutes and schools.

Faculty Electrical Engineering, Mathematics and Computer Science

The Faculty of Electrical Engineering, Mathematics and Computer Science (EEMCS) is known worldwide for its high academic quality and the social relevance of its research programmes. The faculty’s excellent facilities accentuate its international position in teaching and research. Within this interdisciplinary and international setting the faculty employs more than 1100 employees, including about 400 graduate students and about 2100 students. Together they work on a broad range of technical innovations in the fields of sustainable energy, telecommunications, microelectronics, embedded systems, computer and software engineering, interactive multimedia and applied mathematics.

Research at the Delft Institute of Applied Mathematics (DIAM) centres around the study of mathematical models arising in science and engineering. This research is both fundamental and applied in nature, and is often inspired by technical applications. The department plays an active role in translating research results into concrete, practical applications. It maintains intensive contacts with other TU Delft departments, the major technological institutes, and the research laboratories of major companies. Within its own subject field, the department provides teaching for the Applied Mathematics BSc and MSc programmes, and also contributes to the teaching of mathematics courses within other academic programmes at the TU Delft and within national programmes such as “MasterMath”.
The Delft Institute of Applied Mathematics consists of six research groups: Analysis, Mathematical Physics, Numerical Analysis, Applied Probability, Statistics, and Optimisation. More information about the Delft Institute of Applied Mathematics can be found at http://www.ewi.tudelft.nl/en/the-faculty/departments/applied-mathematics/.

The Applied Probability group is one of the key research groups at Delft Institute of Applied Mathematics (DIAM), which forms an integral part of the Faculty of Electrical Engineering, Mathematics and Computer Science (EEMCS). The group performs a broad spectrum of research in the areas mathematical statistical physics, interacting particle systems, ergodic theory, finance and risk.
An important common theme of the institute it partial differential equations. The candidate preferably has a research area in probability that connects to the area interacting particle systems and  their connections with partial differential equations such as e.g. (but not limited to) hydrodynamic limits, large deviations, fluctuation fields, and singular stochastic partial differential equations such as the KPZ equation.