The Tracy-Widom distribution

The Tracy-Widom distribution describes the probability of the largest value (or top score) emerging in certain large, complex systems, like the highest eigenvalue of a random matrix. It captures how extreme outcomes fluctuate in contexts such as physics, statistics, and data analysis. Instead of a common bell curve, it has a distinctive shape emphasizing rare but significant deviations on the high end. This distribution helps us understand the behavior of maximum values in large datasets governed by complex randomness, especially when analyzing the limits of such systems.