Finite Size Fluctuations in Interacting Particle Systems

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.