J. MateusGabriel TéllezFrédéric van Wijland2026-03-222026-03-22202510.1103/22b9-4q39https://doi.org/10.1103/22b9-4q39https://andeanlibrary.org/handle/123456789/78527We endow the elements of a random matrix drawn from the Gaussian unitary ensemble with a Dyson Brownian motion dynamics. We initialize the dynamics of the eigenvalues with all of them lumped at the origin, but one outlier. We solve the dynamics exactly, which gives us a window on the dynamical scaling behavior at and around the Baik-Ben Arous-Péché transition. Amusingly, while the statics is well known and accessible via the Hikami-Brézin integrals, our approach for the dynamics is explicitly based on the use of orthogonal polynomials.enStatistical physicsMathematicsScalingGaussianUnitary stateDynamics (music)Random matrixEigenvalues and eigenvectorsGaussian processBrownian motionarticle