A basic introduction to large deviations: Theory, applications, simulations

Understand

The theory of large deviations deals with the probabilities of rare events (or fluctuations) that are exponentially small as a function of some parameter, e.g., the number of random components of a system, the time over which a stochastic system is observed, the amplitude of the noise perturbing a dynamical system or the temperature of a chemical reaction.

• The theory has applications in many different scientific fields, ranging from queuing theory to statistics and from finance to engineering.
• It is also increasingly used in statistical physics for studying both equilibrium and nonequilibrium systems.
• In this context, deep analogies can be made between familiar concepts of statistical physics, such as the entropy and the free energy, and concepts of large deviation theory having more technical names, such as the rate function and the scaled cumulant generating function.