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Event-by-event fluctuations of the kaon to pion number ratio innucleus-nucleus collisions are studied within the statistical hadron-resonancegas model (SM) for different statistical ensembles and in theHadron-String-Dynamics (HSD) transport approach. We find that the HSD model canqualitatively reproduce the measured excitation function for the $K/\pi$ ratiofluctuations in central Au+Au (or Pb+Pb) collisions from low SPS up to top RHICenergies. Substantial differences in the HSD and SM results are found for thefluctuations and correlations of the kaon and pion numbers. These predictionsimpose a challenge for future experiments.

Fluctuations of the $K/\pi$ Ratio in Nucleus-Nucleus Collisions: Statistical and Transport Models