Convolutions, factorial cumulants and intermittency

It is demonstrated that if multiplicity distributions convolute as a function of a given variable (e.g. rapidity interval), then that variable also shows a true intermittency effect - apparent absence of scale - with a power-law singularity as the variable approaches zero. The intermittency exponents in this case are φqK = q − 1. A simple test for intermittency is proposed making use of the additive property of factorial cumulants for statistically independent subpopulations.