The universal time-dependence of the mean-square displacement for motion in a random energy landscape with equal minima is evaluated analytically and numerically in the percolation path approximation (PPA), which was recently shown by extensive computer simulations in two and three dimensions [Dyre and Schr~ler, cond-mat/9601052] to be more accurate than the standard effective medium approximation (EMA). According to the PPA the universal mean-square displacement in dimensionless units as function of time varies as 1 / In 2 ( t-~ ) for t ~ 0. This implies a quite different short-time behavior than predicted by the EMA, where the universal mean-square displacement varies as 1/ln(t -t) at short times [Dyre and Jacobsen, Phys. Rev. E 52 (1995) 2429].

This paper presents a calculation of the time dependence of the mean-square displacement for symmetric random energy barrier hopping models at low temperatures, where the frequency dependence of the normalized difFusion constant D becomes universal, i.e. , independent of the energy barrier probability distribution [J. C. Dyre

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