Finite Size Fluctuations in Interacting Particle Systems

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.

7 pages, 3 figures

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• First Passage Properties of the Polya Urn Process
• Finite Size Effects in Addition and Chipping Processes
• Supercluster states and phase transitions in aggregation-fragmentation processes
• Noise induced oscillations in non-equilibrium steady state systems
• Simple evolving random graphs
• Dynamic Space Filling