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It is proposed that the rate of relaxation in a liquid is better described bythe geometric mean of the van Hove distribution function, rather than thestandard arithmetic mean used to obtain the mean squared displacement. Thedifference between the two means is shown to increase significantly with anincrease in the non-Gaussian character of the displacement distribution.Preliminary results indicate that the geometric diffusion constant results in asubstantial reduction of the deviation from Stokes-Einstein scaling.

The Geometric Mean Squared Displacement and the Stokes-Einstein Scaling in a Supercooled Liquid