the Wigner semicircle law

The Wigner semicircle law describes how the eigenvalues (numbers associated with a matrix that reveal its properties) of large random symmetric matrices distribute. When you generate many such matrices and look at their eigenvalues, they tend to follow a specific pattern resembling a semicircle, with most eigenvalues clustered near the center and fewer toward the edges. This pattern is universal for large random matrices from certain classes, meaning it appears regardless of the specific details, providing a fundamental insight into complex systems like quantum physics, number theory, and data science.