BBP transition     random-matrices

This simulation uses WebAssembly and the Eigen library to compute eigenvalues of a (modified) Gaussian Orthogonal Ensemble (GOE) matrix. We introduce a rank-1 perturbation governed by a parameter $\theta$: $$A\mapsto A + \theta \cdot e_1e_1^T,$$ where $A$ is the original GOE matrix, and $e_1$ is the first basis vector. There is the BBP phase transition phenomenon: for large enough $|\theta|$, the top eigenvalue “spikes” out of the traditional GOE spectrum.