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Derivation of mean-field equations for stochastic particle systems

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  • Grosskinsky, Stefan
  • Jatuviriyapornchai, Watthanan

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.

Suggested Citation

  • Grosskinsky, Stefan & Jatuviriyapornchai, Watthanan, 2019. "Derivation of mean-field equations for stochastic particle systems," Stochastic Processes and their Applications, Elsevier, vol. 129(4), pages 1455-1475.
    • Handle: RePEc:eee:spapps:v:129:y:2019:i:4:p:1455-1475
    DOI: 10.1016/j.spa.2018.05.006
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    References listed on IDEAS

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    1. Feng, S. & Zheng, X., 1992. "Solutions of a class of nonlinear master equations," Stochastic Processes and their Applications, Elsevier, vol. 43(1), pages 65-84, November.
    2. Armendáriz, Inés & Grosskinsky, Stefan & Loulakis, Michail, 2013. "Zero-range condensation at criticality," Stochastic Processes and their Applications, Elsevier, vol. 123(9), pages 3466-3496.
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    Cited by:

    1. Düring, Bertram & Georgiou, Nicos & Merino-Aceituno, Sara & Scalas, Enrico, 2022. "Continuum and thermodynamic limits for a simple random-exchange model," Stochastic Processes and their Applications, Elsevier, vol. 149(C), pages 248-277.

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