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PhD in Random Networks: How Does Network Structure Affect Phase Transitions in Spreading and Consensus Processes?

Project 2583 · Eindhoven University of Technology (TU/e) · Department of Mathematics and Computer Science

Application workspace

Save this opportunity and prepare around its actual requirements. Confirm deadlines and eligibility at the original source.

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Country or region
Netherlands
Application deadline
2026-12-02 (confirm the exact time with the source)
Funding
Three full-time salaried PhD positions for four years; EUR 3,204–4,051 gross/month (Dutch university scale P), plus 8% holiday allowance and 8.3% year-end bonus, pension and other employee benefits. International staff immigration support is offered; the expat tax compensation scheme is subject to individual eligibility and its value must be confirmed.

The research opportunity

Research and team

The ERC Advanced Grant project Dynamics on and of Random Graphs (Dynamics.oRG), led by Professor Remco van der Hofstad, seeks three PhD candidates to study phase transitions of stochastic processes on random graphs. The processes include models of infection spread and consensus. The research challenge is to understand how randomness in the graph environment interacts with the randomness of the processes occurring on it and whether, when and why the environment changes phase transitions.

The project aims to build a deep mathematical understanding of these phenomena. Candidates work on their own project while collaborating with PhD students, postdoctoral researchers and key collaborators, and contribute to societal impact of network theory.

Eligibility, appointment and application

  • Applicants need a master's or equivalent university degree in Mathematics, a research-oriented attitude, English at C1 level, ability to work in an interdisciplinary team and interest in industrial collaboration, and motivation to develop teaching skills.
  • The full-time fixed-term appointment lasts four years with an intermediate assessment after nine months.
  • Teaching occupies at least 10 percent of the four-year appointment and at most 15 percent in each year.
  • Salary is EUR 3,204–4,051 gross per month under Dutch university scale P, plus an 8 percent holiday allowance and 8.3 percent year-end bonus.
  • Benefits include ABP pension, leave options, training, and commuting/home-working/internet allowances.
  • TU/e offers staff immigration support; any expat tax compensation depends on individual eligibility.
  • Apply online by 2 December 2026 at 23:59 Europe/Amsterdam; email and postal applications are not processed.
  • Submit a cover letter, CV with publication list and contact details for three references.
  • Contact Professor Remco van der Hofstad.

Training and practical considerations

The vacancy does not assign a specific model, theorem or application to each of the three positions, nor state review criteria or the doctoral registration route. EURANDOM and the department offer a probability and statistics research environment; the local random-graphs course illustrates possible training, not a required course for these positions. The Netherlands’ €1,000–€1,500 monthly student budget is a broad dated benchmark, not an employee net-pay estimate; tax, pension, health insurance and housing costs must be considered separately.

Research and application brief

Report generated: . This date does not confirm that recruitment remains open.

Information updated: . Recheck the original notice before applying.

Show report contents

PhD in Random Networks: How Does Network Structure Affect Phase Transitions in Spreading and Consensus Processes?

Quick Decision

This is a three-position, four-year salaried mathematics PhD recruitment within an ERC Advanced Grant project. The scientific focus is how the randomness of a graph environment interacts with stochastic processes on it, including infection spread and consensus, and when that interaction changes phase-transition behaviour. The strongest formal match is a mathematics master’s graduate with probability or related theoretical preparation, C1 English, research motivation, collaborative skills and interest in teaching and industrial interaction. The employer lists €3,204–4,051 gross per month, an 8% holiday allowance, an 8.3% year-end bonus, a nine-month review and a teaching minimum of 10% across the appointment, with no more than 15% in any year. Apply online by 2 December 2026 at 23:59 Europe/Amsterdam; email and postal applications are not processed. The main question before applying is how the three individual research topics differ and whether applicants may express preferences. Official vacancy · application form

Recommendation: Strong but verify fit. The mathematical theme and senior probability group are clear, and the salary is a staff contract rather than an unspecified studentship. However, the notice does not map each vacancy to a separate topic, specify the nine-month assessment criteria or describe the precise doctoral registration/training arrangement. Confirm current vacancy status and the application deadline in the employer system.

Research Problem and Doctoral Work

Random-graph models combine uncertainty in network structure with randomness in the process evolving on that network. In this project, the graph is not just a static background: the research asks whether the graph environment itself changes the threshold or qualitative behaviour of processes such as epidemics and consensus. The advertised goal is rigorous mathematical understanding of those interactions and their phase transitions. Each candidate develops an individual project while collaborating with other doctoral researchers, postdoctoral researchers and external collaborators; the vacancy also mentions societal impact of network theory without promising a particular deployment. Official project vacancy · ERC award list

The project listing does not assign a specific model, theorem or application area to each of the three hires. Recent group work gives useful examples of nearby technical directions: local convergence on dynamic community graphs, giant-component structure, percolation critical windows, and epidemic dynamics on changing networks. These papers are context for a discussion with the supervisor, not a guarantee that any one becomes a PhD topic. Dynamic random intersection graphs · random digraph connectivity · scale-free percolation · SIR on dynamic graphs

School, Programme and Field Context

The employer is Eindhoven University of Technology (TU/e), in its Department of Mathematics and Computer Science. EURANDOM is part of the department’s probability and statistics environment, which provides relevant seminars and research interactions. The advertised job is a salaried employee appointment; the vacancy does not spell out the formal doctoral registration route, doctoral school, or any additional course-credit requirement. Confirm the formal degree and supervision arrangement in the contract or with the department. Department profile · EURANDOM profile

TU/e’s Random Graphs course illustrates local mathematical training in the topic, combining graph models, phase transitions, programming, experiments and proof-based reasoning. It is a course description, not a commitment that these PhD hires will take it. QS lists TU/e at 152 in the 2027 overall world ranking; this is an institution-wide position, not a mathematics ranking. The official research portal locates the university in Eindhoven, Netherlands. Random Graphs course · QS overall ranking · institutional address

Supervisor and Lab Assessment

Professor Remco van der Hofstad is a senior probability researcher at TU/e; the official profile lists a large research output and work in random graphs and network processes. The ERC award record identifies him and TU/e as the principal investigator and host for Dynamics.oRG. That confirms the grant identity and institutional setting, but not the internal distribution of supervision among three candidates or the exact resources each receives. Supervisor profile · ERC award record

Recent papers show a coherent combination of local approximations, global graph structure and threshold phenomena. The 2025 dynamic random-intersection-graph paper extends community models by allowing groups to alternate between active and inactive states, then studies local convergence and the largest component. The random-digraph paper asks when global giant-component properties are approximately determined by local limits. The 2025 percolation paper identifies critical windows across several scale-free graph models. These contributions suggest a mathematically rigorous group, but they do not establish a prescribed candidate project. 2025 dynamic intersection graph paper · 2025 random-digraph paper · 2025 percolation paper

Research Direction and Field Outlook

Dynamic networks and stochastic processes are active areas because real systems change while contagion, information or opinions move through them. A central technical tension is that a static approximation may miss feedback between network evolution and the process; model choices can shift epidemic thresholds. The group’s recent paper on network growth explicitly compares models and illustrates that the epidemic conclusions may depend on assumptions about how networks form. Applicants can discuss how they reason about local weak limits, branching-process approximations, critical windows, coupling, concentration or simulation, while distinguishing their own preparation from project requirements. Network growth and epidemic thresholds

The strongest career transfer is rigorous probability and stochastic modelling, supported by computation and communication. The Brainport region is a high-tech and research-intensive environment, offering adjacent routes in modelling, analytics, software and R&D. Regional job portals describe that ecosystem, but they do not show that probability PhD graduates are in demand or guarantee placements. A more direct professional path is academic research in probability, networks and mathematical modelling. Brainport career context

Funding, Application and Living Cost

The listing advertises three full-time salaried positions for four years, with a nine-month review. Gross pay is €3,204–4,051 per month under Dutch university scale P, plus 8% holiday allowance and 8.3% year-end bonus. It also lists an ABP pension, leave options, training, commuting/home-working/internet allowances, international-staff immigration support and an expat-tax compensation scheme subject to eligibility. The vacancy does not state take-home pay, an individual tax result, or whether any grant-linked research expense budget is available to each candidate. Official vacancy

The application form is online only. The vacancy asks for a cover letter and a CV with publications and contact details for three references. It also asks about mathematical qualifications, prior experience with probability/statistical mechanics/random graphs, and teamwork. The employer page’s deadline is 2 December 2026, 23:59 Amsterdam time. Application form

The Netherlands’ national study portal gives €1,000–1,500 per month as a broad student-cost range and reports an average room range of €450–1,000; it notes the 2024 source year. Another national housing page gives about €550 as a Netherlands-wide average room cost, while Eindhoven municipal advice is student-oriented. These figures are not employee-specific, and room availability and utilities vary. The stated gross salary appears materially above student-cost benchmarks, but compare it with net pay, mandatory health insurance, housing, pension deductions and relocation costs before treating it as disposable income. National student budget · housing guidance · Eindhoven housing information

Applicant Fit and Preparation

Required: a master’s or equivalent university degree in Mathematics; C1 English; research orientation; ability to collaborate in an interdisciplinary team; interest in industrial collaboration; and motivation to develop teaching skills. Application evidence: cover letter, CV/publication list and three referees, submitted through the online form. The form’s questions on probability, statistical mechanics and random graphs are useful indicators of subject relevance but should not be converted into a formal years-of-experience threshold absent one in the notice. Official vacancy · application form

Suggested preparation: explain one proof-based project and one computational or applied project; identify mathematical questions you find interesting about changing network structure; and ask how applicants can indicate preferences across the three positions. Teaching motivation and collaboration are named expectations. No particular programming language, language certificate provider or specific random-graph model is listed as mandatory.

Next Actions and Questions to Verify

Before applying: ask whether there are three distinct research directions and how applicants are matched; confirm that the online system has received all three referees’ details; and request the nine-month review criteria.

At interview: ask about weekly supervision, seminar participation, computational resources, paper-reading expectations, and the balance between theorem development, simulation and collaboration with external partners.

Before accepting: confirm the doctoral registration/degree route, salary step progression, teaching timetable and cap, eligibility and expected value of the expat tax scheme, pension deductions, and immigration support timeline.

Evidence and Sources

Project and recruitment

School, training and research environment

Supervisor and recent research

Living costs and careers

Sources

The listing may come from a university or recruitment platform. Check the notice and official sources in the report for current application requirements. View the recruitment source

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