Scaling limit for interacting Ornstein-Uhlenbeck processes
The problem of describing the bulk behavior of an interacting system consisting of a large number of particles comes up in different contexts. See for example  for a recent exposition. In  one of the authors considered the case of interacting diffusions on a circle and proved that the density of particles evolves according to a nonlinear diffusion equation. The interacting particles evolved according to a generator that was symmetric in equilibrium. In this article we consider interacting Ornstein-Uhlenbeck processes. Here the diffusion generator is not symmetric relative to the equilibrium and the earlier methods have to be modified considerably. We use some ideas that were employed in  to extend the central limit theorem from the symmetric to nonsymmetric cases.
KeywordsNeural Network Statistical Physic Complex System Nonlinear Dynamics Limit Theorem
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