Random energies, random coordination numbers, the Vogel-Fulcher law, and non-exponential relaxation

The collective dynamics of particles in random energies and with a narrow distributed random coordination number shows a dynamical transition. The characteristic macroscopic time scale averaged over the coordination number and the energy distribution diverges with an essential singularity, i.e. as the celebrated Vogel-Fulcher law which is widely used in the treatment of experimental data for the viscosity and relaxation times of glass forming liquids.