The probability group in Durham is actively involved in many areas of modern probability theory and its applications, including connections with analysis, combinatorics, geometry, statistics, and theoretical physics; see individual interests below.
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Stochastic analysis, particularly rough path theory and its applications in stochastic filtering and mathematical finance.
Statistical mechanics and random graphs, with a focus on understanding phase transitions and critical behaviour. In particular, the effect of perturbing these models with a random external field.
Random tiling models, six-vertex model, integrable probability, and KPZ Universality.
Stochastic analysis, random dynamical systems, ergodic theory, nonlinear expectations, and time series, focusing on ergodicity of non-stationary processes (periodic, quasi-periodic) and applications in statistics and non-additive probability.
Probability theory and its applications; probabilistic models and stochastic processes; (random) processes on (random) graphs; spatial random graphs; probabilistic combinatorics.
Statistical mechanics, statistical field theory, and related problems in probability, combinatorics, and theoretical computer science.
Probability and stochastic processes, phase transitions, interacting particle systems, limit theorems, large deviations.
Stochastic differential equations, dynamical systems
Probability theory and applications, especially physics-inspired models: percolation, particle systems, random walks in random environments, including non-homogeneous cases using Lyapunov methods.
Random planar geometry (in particular Schramm-Loewner evolution and the Gaussian free field), branching processes, statistical mechanics, scaling limits, and critical phenomena.
Random graphs, random growth models, random permutations, random matrices and interacting particle systems.
Stochastic analysis & optimal transport on metric-measure spaces: infinite-dimensional interacting SDEs, Wasserstein gradient flows, and geometric tools, with links to KPZ universality, random matrices, and point processes.
Theoretical and applied probability, focusing in history-dependent processes motivated from biological, social and statistical physics. Urn models, random trees and random aggregation models.
Interacting particle systems, branching processes, absorbed Markov processes and their quasi-stationary distributions, piecewise-deterministic Markov processes, population genetics, and applications to radiation transport.
Risk-informed decision making under severe uncertainty using probability bounding, focusing on mathematical foundations and statistical applications in engineering and environmental sciences.
Random walks and their geometry, stochastic processes with constraints or interactions, random spatial graphs, and systems of interacting particles.
How students develop mathematical writing skills; whether peer assessment can help (and whether it’s a good thing anyway); how we talk about examples with students; and e-assessment (particularly STACK).
Stochastic analysis; SPDEs; ergodic theory; dynamics of nonstationary processes; nonlinear expectations; optimal controls; large deviations; stochastic numerics; testing periodicity/quasi-periodicity in finite/infinite dimensions.
Our 2025 Willmore Pure Postgraduate Day celebrated the exciting research in pure mathematics carried out by junior researchers in the Department of Mathematical Sciences.
Find out more about our research, research areas, other members of staff and more.
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