Finite Size Fluctuations in Interacting Particle Systems

TL;DR

This paper investigates how finite size fluctuations influence the behavior of interacting particle systems, revealing that fluctuations can determine outcomes like the final number of particles, which scales logarithmically with system size.

Contribution

It demonstrates that fluctuations significantly impact mean-field dynamics, specifically showing the logarithmic scaling of final particles in a three-species cyclic reaction.

Findings

Final number of particles scales as ln N

Fluctuations dominate as particle count decreases

Applicable to multispecies annihilation processes

Abstract

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.