The Hydrodynamic Limit for Local Mean-Field Dynamics with Unbounded Spins
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.
- Publication:
-
Journal of Statistical Physics
- Pub Date:
- July 2018
- DOI:
- 10.1007/s10955-018-2069-y
- arXiv:
- arXiv:1805.00641
- Bibcode:
- 2018JSP...172..434B
- Keywords:
-
- Interacting diffusions;
- Local mean-field;
- McKean–Vlasov equation;
- Hydrodynamic limit;
- 60J80;
- 60G70;
- 82B44;
- Mathematics - Probability;
- Condensed Matter - Statistical Mechanics;
- 60J80;
- 60G70;
- 82B44
- E-Print:
- 22 pages, several typos corrected