The mean-field theory (MFT) of simple structural glasses which is exact in the limit of infinite spatial dimensions d→∞ offers theoretical insight as well as quantitative predictions about certain features of d=3 systems. In order to more systematically relate the behavior of physical systems to MFT however various finite-d effects need to be accounted for. Although some efforts along this direction have already been undertaken theoretical and technical challenges hinder progress. A general approach to sidestep many of these difficulties consists of simulating minimally-structured models whose behavior smoothly converges to that described by the MFT as d increases so as to permit a controlled dimensional extrapolation. Using this approach we here extract the small fluctuations around the dynamical MFT captured by a standard liquid-state observable the non-Gaussian parameter α2. The results provide insight into the physical origin of these fluctuations as well as a quantitative reference with which to compare observations for more realistic glass formers.
