# Equilibrium fluctuations for lattice gas

Chapter

## Abstract

Professor K. Itô initiated the study of both equilibrium and non-equilibrium fluctuations for a class of systems consisting of a large number of particles [5,6,7]. He especially took a system of independent Brownian particles as a model and derived an infinite-dimensional (*D*’-valued) Ornstein-Uhlenbeck process in the scaling limit of central limit theorem’s type for the counting measures associated with the position of particles. This result was afterward generalized to an interacting case by Spohn [11] in an equilibrium situation. The corresponding law of large numbers, equivalently, the hydrodynamic limit for interacting Brownian particles was established by Varadhan [13].

## Keywords

Drift Term Hydrodynamic Limit Equilibrium Situation Bernoulli Measure Equilibrium Fluctuation
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## References

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© Springer-Verlag Tokyo 1996