Region of validity in theories of diffusion near to the percolation threshold

In theories of classical diffusion near to the percolation threshold two characteristic times can be defined: tau s for the short time and tau h for the hydrodynamic behaviour. Physically tau s < tau h should be fulfilled and the authors suggest this relation as a criterion of validity in such theories. For the effective medium and the self-consistent current relaxation theory the region where this criterion is violated shrinks with dimension d to infinity , but remains finite for all d>2, d=2 is a marginal case concerning the criterion.