Scaling limit for interacting Ornstein-Uhlenbeck processes

Stefano Olla, S. R.S. Varadhan

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Abstract

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 [1] for a recent exposition. In [4] 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 [3] to extend the central limit theorem from the symmetric to nonsymmetric cases.

Original languageEnglish (US)
Pages (from-to)355-378
Number of pages24
JournalCommunications In Mathematical Physics
Volume135
Issue number2
DOIs
StatePublished - Jan 1 1991

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ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics

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