  Fluctuations may govern the fate of an interacting particle system even on
the mean-field level. This is demonstrated via a three species cyclic trapping
reaction with a large, yet finite number of particles, where the final number
of particles N_f scales logarithmically with the system size N, N_f ~ ln N.
Statistical fluctuations, that become significant as the number of particles
diminishes, are responsible for this behavior. This phenomenon underlies a
broad range of interacting particle systems including in particular
multispecies annihilation processes.
