We argue that a crucial determinant of the acceptance dependence of fluctuation measures in heavy-ion collisions is the range of correlations in the momentum space, e.g., in rapidity, ∆ycorr. The value of ∆ycorr ∼ 1 for critical thermal fluctuations is determined by the thermal rapidity spread of the particles at freezeout, and has little to do with position space correlations, even near the critical point where the spatial correlation length ξ becomes as large as 2−3 fm (this is in contrast to the magnitudes of the cumulants, which are sensitive to ξ). When the acceptance window is large, ∆y ∆ycorr, the cumulants of a given particle multiplicity, κ k , scale linearly with ∆y, or mean multiplicity in acceptance, N , and cumulant ratios are acceptance independent. In the opposite regime, ∆y ∆ycorr, the factorial cumulants,κ k , scale as (∆y) k , or N k . We demonstrate this general behavior quantitatively in a model for critical point fluctuations, which also shows that the dependence on transverse momentum acceptance is very significant. We conclude that extension of rapidity coverage proposed by STAR should significantly increase the magnitude of the critical point fluctuation signatures.

We apply stochastic hydrodynamics to the study of charge density fluctuations in QCD matter undergoing Bjorken expansion. We find that the charge density correlations are given by a time integral over the history of the system, with the dominant contribution coming from the QCD crossover region where the change of susceptibility per entropy, χT /s, is most significant. We study the rapidity and azimuthal angle dependence of the resulting charge balance function using a simple analytic model of heavy-ion collision evolution. Our results are in agreement with experimental measurements, indicating that hydrodynamic fluctuations contribute significantly to the measured charge correlations in high energy heavy-ion collisions. The sensitivity of the balance function to the value of the charge diffusion coefficient D allows us to estimate the typical value of this coefficient in the crossover region to be rather small, of the order of (2πT ) −1 , characteristic of a strongly coupled plasma.