Baryon number probability distribution at finite temperature

The probability distribution of the net baryon number is investigated within the functional renormalization group approach. We find that the Roberge-Weiss periodicity related to the Z(3) symmetry of the gluon fields results directly in that, states of the net baryon number $N_B=N\pm 1\mathrm{/}3$ with $N\in \mathbb{Z}$ are prohibited, and only those of $N_B=N$ are possible. By employing the probability distribution of the net baryon number, we also compute the cumulants of the baryon number distribution, which are found to be well consistent with those obtained from the generalized susceptibilities. A question about the relation between the color confinement and the probability distribution of net baryon number is put forward.