  The multiplicity fluctuations of hadrons are studied within the statistical
hadron-resonance gas model in the large volume limit. The role of quantum
statistics and resonance decay effects are discussed. The microscopic
correlator method is used to enforce conservation of three charges -- baryon
number, electric charge, and strangeness -- in the canonical ensemble. In
addition, in the micro-canonical ensemble energy conservation is included. An
analytical method is used to account for resonance decays. The multiplicity
distributions and the scaled variances for negatively and positively charged
hadrons are calculated for the sets of thermodynamical parameters along the
chemical freeze-out line of central Pb+Pb (Au+Au) collisions from SIS to LHC
energies. Predictions obtained within different statistical ensembles are
compared with the preliminary NA49 experimental results on central Pb+Pb
collisions in the SPS energy range. The measured fluctuations are significantly
narrower than the Poisson ones and clearly favor expectations for the
micro-canonical ensemble. Thus, this is a first observation of the recently
predicted suppression of the multiplicity fluctuations in relativistic gases in
the thermodynamical limit due to conservation laws.
