  In assemblies of globally coupled dynamical units, weak noise perturbing
independently the individual units can cause anomalous dispersion in the
synchronized cloud of the units in the phase space.
  When the noise-free dynamics of the synchronized assembly is nonperiodic,
various moments of the linear dimension of the cloud as a function of the noise
strength exhibit multiscaling properties with parameter-dependent scaling
exponents. Some numerical evidence of this peculiar behavior as well as its
interpretation in terms of a multiplicative stochastic process with small
additive noise is provided.
  Universality of the phenomenon is also discussed.
