We investigate properties of the probability distribution of the net quark
number near the chiral crossover transition in the quark-meson model. The
calculations are performed within the functional renormalization group
approach, as well as in the mean-field approximation. We find, that there is a
substantial influence of the underlying chiral phase transition on the
properties of the probability distribution. In particular, for a physical pion
mass, the distribution which includes the effect of mesonic fluctuations,
differs considerably from both, the mean-field and Skellam distributions. The
latter is considered as a reference for a non-critical behavior. A
characteristic feature of the net quark number probability distribution is
that, in the vicinity of the chiral crossover transition in the O(4)
universality class, it is narrower than the corresponding mean-field and
Skellam function. We study the volume dependence of the probability
distribution, as well as the resulting cumulants, and discuss their approximate
scaling properties.Comment: 9 pages, 7 figures. to appear in Phys. Rev. C. Discussion on
differences between the mean-field and FRG results is extende
