Applications of large deviations in disordered systems

Abstract

In this thesis we study the problem of computing probability distribution of rare events on disordered systems, i.e. systems made up of heterogeneous interacting agents, using tools from statistical physics. We explore several areas of statistical physics, from traditional subjects such as the random field Ising model to random walkers on graphs to more recent developments such as systemic risk in financial networks, using simple models to explore how interactions and network structure shape the occurrence of rare events, and how these rare events in turn shape our macroscopic perceptions.

We present exact analytical results using generating functional methods when possible, and propose approximations where needed, and we compare our results with simulations. Finally, we discuss how our models can be modified and extended to answer new questions.

Date of Award	2017
Original language	English
Awarding Institution	King's College London
Supervisor	Reimer Kuhn (Supervisor) & Peter Sollich (Supervisor)