Probability and applications research

Randomness surrounds us, from the motion and collisions of atoms to the arrival of cars at an intersection. Our research seeks to understand this randomness.

Students walking on campus

Probability includes both the theory and application of complex models motivated by other areas of mathematics and statistics, as well as physics, biology, finance and many other applied fields.

Stochastic processes

Probability research often involves studying the stochastic process of a system evolving randomly over time. Researchers can consider how changes to the system affect long term behaviour. For example, in modelling the spread of infectious disease, what methods must we use to reduce transmission rates (eg. vaccination or quarantine) and stop a large scale epidemic? Our research in branching processes aims to develop theories and techniques for answering such questions.

Probability theory

Many complex real-world systems have similar global features, even when their fine details are different. For instance, random networks in everyday life, from the World Wide Web, to social media networks, to power distribution grids, share a surprising “small-world” property. Probability theory shows how randomness can explain the commonalities between these apparently different examples.

Applied probability and stochastic operations research

Our research in applied probability includes optimising systems for performance where there is inherent randomness, also known as stochastic operations research. Examples include minimising waiting times in queues for hospital treatments, maintaining the reliability of telecommunication networks, or managing water flow for hydro-electricity.

Our researchers

Dr Azam Asanjarani

  • Applied probability
  • Queueing theory
  • Markov decision processes

Professor Rachel Fewster

  • Stochastic process models in ecology and population genetics

Dr Ciprian Giurcaneanu

  • Information-theoretic methods for time series

Dr Jesse Goodman

  • Probability theory
  • Scaling limits
  • Random graphs

Associate Professor Simon Harris

  • Probability theory
  • Brownian motion
  • Branching processes

Professor Thomas Lumley

  • Transit modelling

Dr Geoffrey Pritchard

  • Stochastic operations research
  • Applications in electricity markets

Associate Professor Ilze Ziedins

  • Stochastic queueing networks
  • Routing problems
  • Markov decision processes