The linear stability of large complex systems around their stationary points can be studied with random matrix theory. In one common model, the i.i.d. random matrix model, one assumes a simple statistical form for the interactions between distinct elements of a network. Read more
Economists thinking about anything from housing policy to climate change need to model how people make decisions, especially when facing uncertainty and risk. Read more
Economics had its critics even before the financial crisis of a decade ago. Since then doubt has grown over how much economists really know. Much of economics rests on analyses of how individuals – as consumers, or in managing a business, for example – make supposedly optimal decisions in uncertain situations. Read more
Variations in the strength of gravity over the Earth’s surface reflect underlying geophysical changes such as groundwater change, surface vertical deformation, tectonic events, earthquakes and other processes. To study such processes, so-called gravity survey campaigns collect observations made repeatedly at fixed stations. Read more
High-profile data horror stories are becoming increasingly common, from Facebook’s relationship with Cambridge Analytica to the leak of UK diplomatic cables and massive security breaches at some of the world’s biggest companies. Read more
Some of the strongest challenges for numerical weather prediction come from the unsteady nature of certain flows, in particular nocturnal and stable boundary layers. Read more
When steam condenses from vapour into liquid, the water molecules move closely together and the system, from a mathematical point of view, comes to reside in an extremely small portion of the conceptually available phase space. Read more
Telecommunications engineers and operations researchers aim to manage complex and fluctuating traffic flows through extended networks. Among other techniques, they have exploited results from the theory of large deviations to estimate the likelihood that a demand in service will overflow the available resources. Read more
Systems out of equilibrium typically carry macroscopic currents of particles, mass or energy. Thermodynamic uncertainty relations offer universal bounds linking such currents and their statistical fluctuations to other system properties, especially entropy production. Read more
Probability theory emerged in the second half of the 17th century as a way to think about monetary gambles, and how to choose wisely when facing uncertainty. Early thinking suggested that people would act so as to maximise the expected change in wealth – an average over all possible outcomes. Read more
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