Derivation of mean-field equations for stochastic particle systems

Abstract

We study stochastic particle systems on a complete graph and derive effective mean-field rate equations in the limit of diverging system size, which are also known from cluster aggregation models. We establish the propagation of chaos under generic growth conditions on particle jump rates, and the limit provides a master equation for the single site dynamics of the particle system, which is a non-linear birth death chain. Conservation of mass in the particle system leads to conservation of the first moment for the limit dynamics, and to non-uniqueness of stationary distributions. Our findings are consistent with recent results on exchange driven growth, and provide a connection between the well studied phenomena of gelation and condensation.

arXiv comment26 pages

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Cited by in corpus (7)

• The exchange-driven growth model: basic properties and longtime behavior
• Mathematical Theory of Exchange-driven Growth
• Continuum and thermodynamic limits for a simple random-exchange model
• Rare event simulation for stochastic dynamics in continuous time
• Entropic curvature and convergence to equilibrium for mean-field dynamics on discrete spaces
• Self-similar behavior of the exchange-driven growth model with product kernel
• Size-biased diffusion limits and the inclusion process