Large Deviations Principle

The Large Deviations Principle (LDP) is a mathematical framework that studies the likelihood of rare events in a system. It quantifies how quickly the probability of an unusual outcome decreases as the system size or the number of observations grows. Essentially, LDP provides tools to assess the risk of significant deviations from typical behavior, often showing that such rare events become exponentially less probable as the system becomes larger. This principle helps in fields like statistics, physics, and finance to understand and predict the chances of unlikely but impactful events.