Proceedings of 4th International Workshop "Critical Point and Onset of Deconfinement", July 9-13, 2007, Darmstadt, Germany: 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
