  Smoluchowski's coagulation kinetics is here shown to fail when the coalescing
species are dilute and transported by a turbulent flow. The intermittent
Lagrangian motion involves correlated violent events that lead to an unexpected
rapid occurrence of the largest particles. This new phenomena is here
quantified in terms of the anomalous scaling of turbulent three-point motion,
leading to significant corrections in macroscopic processes that are critically
sensitive to the early-stage emergence of large embryonic aggregates, as in
planet formation or rain precipitation.
