Large deviations theory

Large deviations theory is a branch of probability theory that deals with the study of rare events—specifically, events that deviate significantly from expected behavior. It provides a mathematical framework for quantifying the probabilities of these rare deviations from the average or typical outcome of a stochastic process. The fundamental ideas in large deviations theory include: 1. **Rate Functions**: These are functions that describe the exponential decay rate of the probabilities of rare events.