Tracy–Widom distribution

The Tracy-Widom distribution is a probability distribution that describes the behavior of the largest eigenvalues in random matrices, particularly those of large complex systems. It's especially important in fields like physics, finance, and statistics, as it helps understand phenomena such as fluctuations in large-scale phenomena, like energy levels in quantum mechanics or the performance of complex networks. When you study many random matrices, the distribution of their largest values tends to follow the Tracy-Widom curve, revealing insights into underlying structures and patterns in various scientific and mathematical contexts.