  Non-Gaussian nature of the probability distribution of particles'
displacements in the supercooled temperature regime in glass-forming liquids
are believed to be one of the major hallmarks of glass transition. It is
already been established that this probability distribution which is also known
as the van Hove function show universal exponential tail. The origin of such an
exponential tail in the distribution function is attributed to the hopping
motion of particles observed in the supercooled regime. The non-Gaussian nature
can also be explained if one assumes that the system has heterogeneous dynamics
in space and time. Thus exponential tail is the manifestation of dynamic
heterogeneity. In this work we directly show that non-Gaussanity of the
distribution of particles' displacements occur over the dynamic heterogeneity
length scale and dynamical behaviour course grained over this length scale
becomes homogeneous. We study the non-Gaussianity of van Hove function by
systematically coarse graining at different length scale and extract the length
scale of dynamic heterogeneity at which the shape of the van Hove function
crosses over from non-Gaussian to Gaussian. The obtained dynamic heterogeneity
scale is found to be in very good agreement with the scale obtained from other
conventional methods.
