Gaussian Orthogonal Ensemble (GOE)

The Gaussian Orthogonal Ensemble (GOE) is a mathematical concept used in random matrix theory. It involves collections of large matrices with randomly assigned entries that are symmetric, meaning the matrix is mirrored along its diagonal. The entries follow a normal (Gaussian) distribution, with specific statistical properties. GOE helps scientists understand complex systems where interactions are random but symmetric, such as energy levels in heavy atoms or vibrations in disordered materials. It provides a framework to analyze patterns and statistical behavior of eigenvalues, aiding research in physics, mathematics, and related fields.