  Standard approach to dynamical random matrix models relies on the description
of trajectories of eigenvalues. Using the analogy from optics, based on the
duality between the Fermat principle(trajectories) and the Huygens principle
(wavefronts), we formulate the Hamilton-Jacobi dynamics for large random matrix
models. The resulting equations describe a broad class of random matrix models
in a unified way, including normal (Hermitian or unitary) as well as strictly
non-normal dynamics. HJ formalism applied to Brownian bridge dynamics allows
one for calculations of the asymptotics of the Harish-Chandra-Itzykson-Zuber
integrals.
