  Motivated by the relation existing between the gluon density in a hadron and
the multiplicity of the particles measured in the final state of hadron-nucleus
collisions, we study systematically the fluctuations of the gluon density in
onia, which are the simplest dilute hadrons, of different sizes and at various
rapidities. We argue that the small and the large-multiplicity tails of the
gluon distributions present universal features, which should translate into
properties of the multiplicity of the particles measured in the final state of
high-energy proton-nucleus collisions, or of deep-inelastic scattering at a
future electron-ion collider. We propose simple physical pictures of the rare
events populating the tails of the multiplicity distribution that allow us to
derive analytical formulas describing these universal behaviors, and we compare
them to the results of Monte Carlo simulations.
