Counting hot/cold spots in quark-gluon plasma

We study how local fluctuations in the initial states of relativistic heavy-ion collisions manifest in the correlations between different orders of harmonic moments of the density profiles, particularly those involving only odd harmonics that arise purely from initial-state fluctuations. We find the strengths of those correlations are sensitive to the number of hot and cold spots in the initial states. Hydrodynamic evolution of the fireball translates initial-state geometric anisotropies as well as their correlations into final-state momentum anisotropies and correlations. We conclude that the measurement of the correlations between different harmonic moments of final-state azimuthal distribution can be employed to quantify the inhomogeneity of the initial density profiles such as the population of hot and cold spots that are produced in high-energy nuclear collisions.