Large Deviations Theory

Large Deviations Theory studies how and why rare events occur in probability systems. It quantifies the chances of significant deviations from typical behavior, like extreme fluctuations in stock prices or unexpected failure of systems. Essentially, it provides mathematical tools to estimate how unlikely certain outcomes are, especially those far from the average or expected result. This helps in understanding and managing risks associated with rare but impactful events in fields like finance, engineering, and physics.