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The Hydrodynamic Limit for Local Mean-Field Dynamics with Unbounded Spins

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Abstract

We consider the dynamics of a class of spin systems with unbounded spins interacting with local mean-field interactions. We prove convergence of the empirical measure to the solution of a McKean–Vlasov equation in the hydrodynamic limit and propagation of chaos. This extends earlier results of Gärtner, Comets and others for bounded spins or strict mean-field interactions.

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Notes

  1. Arguments developed in Sect. 2 require smoothness and certain growth properties of \(\psi ^\prime \) at infinity and could be readily extended to a larger class of local potentials.

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Authors and Affiliations

  1. Institut für Angewandte Mathematik, Rheinische Friedrich-Wilhelms-Universität, Endenicher Allee 60, 53115, Bonn, Germany

    Anton Bovier

  2. William Davidson Faculty of Industrial Engineering and Management, Technion, 32000, Haifa, Israel

    Dmitry Ioffe

  3. Boston Consulting Group, Im Mediapark 8, 50670, Cologne, Germany

    Patrick Müller

Authors
  1. Anton Bovier
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  2. Dmitry Ioffe
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  3. Patrick Müller
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Corresponding author

Correspondence to Anton Bovier.

Additional information

A.B. is partially supported through the German Research Foundation in the Collaborative Research Center 1060 “The Mathematics of Emergent Effects”, the Hausdorff Center for Mathematics (HCM), and the Cluster of Excellence “ImmunoSensation” at Bonn University.

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Bovier, A., Ioffe, D. & Müller, P. The Hydrodynamic Limit for Local Mean-Field Dynamics with Unbounded Spins. J Stat Phys 172, 434–457 (2018). https://doi.org/10.1007/s10955-018-2069-y

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  • DOI: https://doi.org/10.1007/s10955-018-2069-y

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