PhD Position: Strongly Correlated Percolation Models Monash University in Australia

This PhD project at Monash University's School of Mathematics focuses on strongly correlated percolation models, a cutting-edge topic at the intersection of probability theory and statistical physics. Percolation theory investigates the connectivity properties of random disordered systems, with a rich history of results for systems exhibiting large-scale independence. Recent advances include the computation of critical exponents and proofs of rotational invariance in two-dimensional systems. However, for systems with strong correlations, the rigorous mathematical theory is still developing, despite significant predictions from physicists.

The aim of this project is to advance the understanding of percolation models with strong correlations, particularly by computing or bounding their critical exponents. This research will contribute to the theoretical foundations of statistical physics and probability, potentially validating or challenging existing physical predictions. The successful candidate will join a vibrant research environment within the School of Mathematics, working under the supervision of Dr. Stephen Muirhead, whose Australian Research Council Future Fellowship funds the position.

Funding is available for domestic students, covering both tuition fees and a stipend. International students will receive a stipend, and are encouraged to apply for a Monash scholarship to cover tuition fees. Applicants should hold an Honours or Masters degree in mathematics, with a research thesis component, and possess a strong background in probability theory. English language proficiency is required for non-native speakers (IELTS 6.5 overall, minimum 6.0 in each component).

The application deadline is February 14, 2026, with an expected start date before September 1, 2026. To apply, send a cover letter, CV, academic transcript, and contact details for two referees to Dr. Stephen Muirhead ([email protected]). Including a copy of your Honours/Masters thesis is encouraged. For more information, visit Dr. Muirhead's academic page and the School of Mathematics postgraduate research site.