The Large Deviations Principle (LDP) is a mathematical framework that provides a way to understand the probabilities of rare events in stochastic processes. It helps quantify how likely it is for a random variable to deviate significantly from its expected value. This principle is particularly useful in fields like statistical mechanics, information theory, and finance. In essence, the LDP states that the probabilities of these rare deviations can be approximated using a rate function, which describes how the likelihood of an event decreases exponentially as the deviation increases. This allows researchers to analyze and predict the behavior of complex systems under extreme conditions.