Finite Size Fluctuations in Interacting Particle Systems
E. Ben-Naim and P.L. Krapivsky
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 $N$, $N_f\sim\ln N$.
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.
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