experimental and theoretical study of fluctuations in strong interactions (see e.g., reviews [@reviewfluc]) is motivated by expectations of anomalies in the vicinity of the onset of deconfinement [@ood] and in the case when the expanding system goes through the transition line between a quark-gluon plasma and a hadron gas phase [@phasetrans]. In particular, a critical point of strongly interacting matter may be accompanied by a characteristic power-law pattern in fluctuations [@critpoint]. A non-monotonic dependence of event-by-event fluctuations on system size and/or center of mass energy in heavy ion collisions would therefore give valuable insight into the phase diagram of strongly interacting matter. Provided the signal survives the subsequent evolution and hadronization of the system (see also [@recomb]). Therefore, in order to asses the discriminating power of proposed measures, for a recent review see [@reviewfluc2], one should firstly study properties of equilibrated sources [@MCEvsData; @res; @VolDep; @vdw] and quantify ‘baseline‘ (or thermal/statistical) fluctuations. Apart from being an important tool in an effort to study a possible critical behavior, the study of fluctuations within the statistical model constitutes also a further test of its validity.

In this paper we make detailed predictions for the momentum space dependence of multiplicity fluctuations. We show 