  We build up a phenomenological picture in terms of the effective dynamics of
a tracer confined in a cage experiencing random hops to capture somec
haracteristics of glassy systems. This minimal description exhibits scale
invariance properties for the small-displacement distribution that echo
experimental observations. We predict the existence of exponential tails as a
cross-over between two Gaussian regimes. Moreover, we demonstrate that the
onset of glassy behavior is controlled only by two dimensionless numbers: the
number of hops occurring during the relaxation of the particle within a local
cage, and the ratio of the hopping length to the cage size.
