Gaussian Unitary Ensemble (GUE)

The Gaussian Unitary Ensemble (GUE) is a mathematical model used to study complex systems, such as energy levels of quantum particles, by representing matrices with random, complex numbers that are symmetric in a specific way. These matrices have properties that make their eigenvalues—special numbers associated with them—spread out in a predictable pattern. GUE helps scientists understand phenomena in physics, statistics, and number theory by analyzing the statistical behavior of these eigenvalues, revealing universal patterns in systems with randomness and symmetry.