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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