Large deviations

Large deviations is a concept in probability and statistics that examines how unlikely certain extreme events are, compared to what is typically expected. It focuses on understanding the probabilities of significant deviations from the average or expected behavior in random processes. For example, if you toss a coin many times, large deviations study the rare cases where you get an unusually high or low number of heads, helping to inform us about the risks and behaviors of complex systems in fields like finance, physics, and telecommunications.