Fluctuation induced equality of multi-particle eccentricities for four or more particles

We discuss eccentricities (ellipticity and triangularity) generated in nucleus-nucleus and proton-nucleus collisions. We define multi-particle eccentricities ϵn{m} which are associated with the n'th angular multipole moment for m particles. We show that in the limit of fluctuation dominance all of the ϵn{m}'s are approximately equal for m⩾4. For dynamics linearly responding to these eccentricities such as hydrodynamics, these relations among eccentricities are translated into relations among flow moments vn{m}. We explicitly demonstrate it with hydrodynamic calculations.