We have studied numerically the decay of the self-dynamic structure fa
ctor (SDSF) for a small particle diffusing in a colloidal glass. We sh
ow that, in line with theoretical predictions, the super-Burnett coeff
icient (characterizing the deviation of the fourth moment of the singl
e particle distribution from its Gaussian value) is finite. However, o
ur results also show that large scale deviations from Fick's law of di
ffusion should still be easy to detect experimentally. These deviation
s take the form of the SDSF decaying algebraically rather than exponen
tially as Fick's law would predict. (C) 1998 American Institute of Phy
sics. [S0021-9606(98)50924-5].