Divergences in the amplitudes of the "long-time tails"

The self-diffusion constant vanishes in a scattering medium approaching a percolation transition, and the shear viscosity diverges near a glass transition. If the dependence of these transport coefficients upon the distance to the transition point $\epsilon$ and upon the frequency $\omega$ is given by a scaling law, it is shown that the "long-time tails" on the correlation functions, whose time integrals give the transport coefficients, diverge. The divergences are expressed in terms of existing critical exponents only. The theory is in reasonable agreement with existing experimental results and with related theories.