The Gaussian Orthogonal Ensemble (GOE) is a statistical model used in random matrix theory. It describes the properties of real symmetric matrices, where the entries are drawn from a Gaussian distribution. GOE is particularly important in understanding the behavior of complex systems, such as those found in quantum mechanics and nuclear physics. In the GOE, the eigenvalues of the matrices exhibit specific statistical properties, such as level repulsion, which means that eigenvalues tend to avoid each other. This phenomenon is observed in various physical systems, including the energy levels of nuclei and quantum dots, making GOE a valuable tool in theoretical physics.