Exact calculation of the probabilities of rare events in cluster-cluster aggregation

We develop an action formalism to calculate probabilities of rare events in cluster-cluster aggregation for arbitrary collision kernels and establish a pathwise large deviation principle with total mass being the rate. As an application, the rate function for the number of surviving particles as well as the optimal evolution trajectory are calculated exactly for the constant, sum and product kernels. For the product kernel, we argue that the second derivative of the rate function has a discontinuity. The theoretical results agree with simulations tailored to the calculation of rare events.