The relevance of higher order cumulants of net baryon number fluctuations for
the analysis of freeze-out and critical conditions in heavy-ion collisions at
LHC and RHIC is addressed. The sign structure of the higher order cumulants in
the vicinity of the chiral crossover temperature might be a sensitive probe and
may allow to elucidate their relation to the QCD phase transition. We calculate
ratios of generalized quark-number susceptibilities to high orders in three
flavor QCD-like models and investigate their sign structure close to the chiral
crossover line.Comment: presented at the International Conference "Critical Point and Onset
of Deconfinement - CPOD 2011", Wuhan, November 7-11, 2011; version to appear
in Cent. Eur. J. Phy
