Communications in Mathematical Physics

, Volume 135, Issue 2, pp 355–378 | Cite as

Scaling limit for interacting Ornstein-Uhlenbeck processes

  • Stefano Olla
  • S. R. S. Varadhan
Article

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.

Keywords

Neural Network Statistical Physic Complex System Nonlinear Dynamics Limit Theorem 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    Deuschel, J.D., Stroock, D.W.: Large deviations. New York: Academic Press 1989Google Scholar
  2. 2.
    De Masi, A., Presutti, E.: Lectures on the collective behavior of particle systems. C.A.R.R. Reports in Mathematical Physics, 5/89, 1989Google Scholar
  3. 3.
    Papanicolaou, G., Varadhan, S.R.S.: Ornstein-Uhlenbeck process in a random potential. Commun. Pure Appl. Math.35, 819–834 (1985)Google Scholar
  4. 4.
    Varadhan, S.R.S.: Scaling limits for interacting diffusions. Commun. Math. Phys.135, 313–353 (1991)Google Scholar

Copyright information

© Springer-Verlag 1991

Authors and Affiliations

  • Stefano Olla
    • 1
  • S. R. S. Varadhan
    • 1
  1. 1.Courant Institute of Mathematical SciencesNew York UniversityNew YorkUSA

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