A Monte Carlo algorithm to measure probabilities of rare events in cluster-cluster aggregation

We develop a biased Monte Carlo algorithm to measure probabilities of rare events in cluster-cluster aggregation for arbitrary collision kernels. Given trajectory with fixed number collisions, the modifies both waiting times between as well sequence using local moves. show that is ergodic by giving protocol transforms an standard valid The can sample order $10^{-40}$ and lower. algorithm's effectiveness sampling low-probability established showing numerical results large deviation function constant-kernel reproduce exact results. It shown obtain functions other kernels, including gelling ones, instanton trajectories atypical times. dependence autocorrelation times, temporal configurational, on different parameters also characterized.