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This research area links the microscopic world of individual interacting components to the macroscopic behaviour of complex systems.

Applied Probability provides the fundamental framework for Statistical Mechanics by explaining how large numbers of interacting parts, such as molecules, fluid vortices, stock traders, neurons, and computer servers, give rise to collective behaviour.

Stochastic Analysis uses tools such as stochastic partial differential equations and Brownian motion to explore how these systems evolve over time by modelling randomness and uncertainty.

Together, these disciplines provide a powerful mathematical framework for analysing systems ranging from chemical physics to financial markets, where large-scale patterns emerge from microscopic interactions.

• ¶Ù°ù J±ð°ù´Ç±ð²Ô W´Ç³Ü³Ù±ð°ù²õ uses ideas from statistical mechanics and stochastic analysis to develop stochastic reduced models that capture the effective dynamics of complex, high‑dimensional systems. These models provide mathematically grounded descriptions of unresolved processes. He also develops efficient rare‑event simulation methods to analyse extreme events in stochastic dynamical systems, with particular interest in climate extremes.
• Dr Jochen Broecker applies the mathematics of probability and nonlinear dynamics to study complex, infinite-dimensional stochastic systems, particularly in the climate and environmental sciences.
• Dr Eviatar Bach applies ideas from applied probability and dynamical systems to climate science, with a particular focus on modelling systems that evolve over time under uncertainty.