  We study how local fluctuations in the initial states of relativistic
heavy-ion collisions manifest themselves in the correlations between different
orders of harmonic moments of the density profiles, particularly those
involving only odd harmonics which purely arise 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.
